Subtitles section
Repeat sentence
Subtitles mode
Full screen
Previous
Next
x 1.0
Playback speed
More

Basic derivative rules (Part 2) | Derivative rules | AP Calculus AB | Khan Academy

Video vocabulary

first

Copy vocabulary

US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

Copy vocabulary

US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

conclusion

Copy vocabulary

US / kənˈklu:ʒn /

UK / kənˈkluʒən /

A2
  • noun
  • End of something; finish
  • Judgment or opinion after thinking for a while
  • Opinion or final judgment at end of book, essay

find

Copy vocabulary

US / faɪnd /

UK / faɪnd /

A1
  • noun
  • Object discovered by chance
  • Things that have been discovered from searching
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

then

Copy vocabulary

US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

right

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

straightforward

Copy vocabulary

US / ˌstreɪtˈfɔ:wəd /

UK / stretˈfɔrwəd /

B1
  • adjecitve
  • Easy to do or understand; not complicated

about

Copy vocabulary

US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

like

Copy vocabulary

US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

what

Copy vocabulary

US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

that

Copy vocabulary

US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

second

Copy vocabulary

US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon

feel

Copy vocabulary

US / fi:l /

UK / fil /

A1
  • verb
  • To be aware of or experience an emotion, sensation
  • To sense through direct contact; touch

plus

Copy vocabulary

US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

actually

Copy vocabulary

US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

ensure

Copy vocabulary

US / ɪn'ʃʊə(r) /

UK / ɛnˈʃʊr /

A2
  • verb
  • To make something sure, certain, or safe

use

Copy vocabulary

US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

write

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

either

Copy vocabulary

US / ˈaɪðə(r) /

UK / ˈiðɚ, ˈaɪðɚ /

A1
  • adjecitve
  • One of two (used when there is a choice of two)
  • adverb
  • (After negative statements) likewise, in addition
  • conjunction
  • Used as the first of two connected things
  • determiner
  • Used as the first of two connected things
  • pronoun
  • The one or the other

here

Copy vocabulary

US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

try

Copy vocabulary

US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

once

Copy vocabulary

US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

probably

Copy vocabulary

US / ˈprɒbəbli /

UK / ˈprɑbəbli /

A1
  • adverb
  • That is likely to happen or be true

guess

Copy vocabulary

US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

dimension

Copy vocabulary

US / daɪˈmenʃn /

UK / dɪˈmɛnʃən, daɪ- /

B1
  • noun
  • Number of planes (X, Y, Z axes) an object has
  • Measurement in space, e.g. length or diameter
  • Scope, extent or size of something abstract

will

Copy vocabulary

US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

true

Copy vocabulary

US / tru: /

UK / tru: /

A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

third

Copy vocabulary

US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

sort

Copy vocabulary

US / sɔ:t /

UK / sɔrt /

A1
  • noun
  • Group or class of similar things or people
  • verb
  • To organize things by putting them into groups
  • To deal with things in an organized way

any

Copy vocabulary

US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

think

Copy vocabulary

US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

something

Copy vocabulary

US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

another

Copy vocabulary

US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

sometimes

Copy vocabulary

US / ˈsʌmtaɪmz /

UK / ˈsʌmˌtaɪmz /

A1
  • adverb
  • Only at certain times; occasionally

front

Copy vocabulary

US / frʌnt /

UK / frʌnt /

A1
  • adjecitve
  • Opposite of back; the forward part of an object
  • noun
  • Behavior not showing a person's true feelings
  • Area where fighting in a war is happening
  • Place where air of different temperatures meets
  • verb
  • To have the forward part facing something
  • To lead a group of people, usually a band

put

Copy vocabulary

US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

rearrange

Copy vocabulary

US / ˌri:ə'reɪndʒ /

UK / ˌriəˈrendʒ /

B1
  • verb
  • To rethink a plan, event for a time and place
  • To put into a new order for something to happen

two

Copy vocabulary

US / tu: /

UK / tu /

A1
  • number
  • 2

rest

Copy vocabulary

US / rest /

UK / rɛst /

A1
  • noun
  • Time when one relaxes, sleeps, or is inactive
  • State in which there is a lack of motion
  • Part of something remaining after some was used
  • verb
  • To stop working or avoid activity to recover
  • (Of dead person) to lie in a grave
  • To lean, support or place something against
  • To not be tired because you had enough sleep

throughout

Copy vocabulary

US / θru:ˈaʊt /

UK / θruˈaʊt /

A2
  • adverb
  • From the beginning of something until the end
  • preposition
  • Over/across an entire place/thing; in every part

and

Copy vocabulary

US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

base

Copy vocabulary

US / beɪs /

UK / bes /

A2
  • noun
  • Place military personnel live, train, and operate
  • Bottom part of an object that touches a surface
  • Unit of counting, e.g. 10 for counting
  • Most important idea or ingredient to add others
  • Origin or start from which something came
  • Main place where an organization or a person works
  • verb
  • To use as the starting point or origin for
  • To have as the main location for (company, etc.)

hopefully

Copy vocabulary

US / ˈhəʊpfəli /

UK / ˈhopfəli /

A2
  • adverb
  • In a manner wishing something to happen

lot

Copy vocabulary

US / lɒt /

UK / lɑt /

A1
  • noun
  • What happens to a person in life from chance; fate
  • A group of people seen together
  • Item for sale at an auction
  • Small area of land used for a purpose e.g. parking

pen

Copy vocabulary

US / pen /

UK / pɛn /

A2
  • noun
  • Small fenced area where people or animals are kept
  • Writing tool that uses ink
  • verb
  • To put animals, people in a fenced or closed area
  • To write (a song, love letter, etc.)

from

Copy vocabulary

US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

out

Copy vocabulary

US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

over

Copy vocabulary

US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

minus

Copy vocabulary

US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

little

Copy vocabulary

US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

let

Copy vocabulary

US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

might

Copy vocabulary

US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

the

Copy vocabulary

US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

subtraction

Copy vocabulary

US / səb'trækʃn /

UK / səbˈtrækʃən /

B2
  • noun
  • Act of taking one value away from another

this

Copy vocabulary

US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

make

Copy vocabulary

US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

other

Copy vocabulary

US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

one

Copy vocabulary

US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

also

Copy vocabulary

US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

you

Copy vocabulary

US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

although

Copy vocabulary

US / ɔ:lˈðəu /

UK / ɔlˈðo /

A1
  • conjunction
  • Despite the fact that; however

core

Copy vocabulary

US / kɔ:(r) /

UK / kɔr, kor /

A2
  • noun
  • Important central part of something
  • verb
  • To take out the central section of a fruit

have

Copy vocabulary

US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

last

Copy vocabulary

US / lɑ:st /

UK / læst /

A1
  • adjecitve
  • Most recent; the latest
  • The one before
  • adverb
  • Final; with nothing following; after all others
  • Most recent; the latest
  • determiner
  • The one at the end
  • verb
  • To remain or continue for a certain period of time

prime

Copy vocabulary

US / praɪm /

UK / praɪm /

A2
  • adjecitve
  • Concerning the highest in quality or value
  • Concerning the highest level of achievement
  • Most important, chief importance in value
  • verb
  • To get a person ready for; prepare someone
  • To coat with paint to prepare it for the main coat

see

Copy vocabulary

US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

could

Copy vocabulary

US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

know

Copy vocabulary

US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

all

Copy vocabulary

US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

top

Copy vocabulary

US / tɒp /

UK / tɑp /

A1
  • adjecitve
  • Being good or great; excellent
  • Being the most in degree or quality
  • noun
  • Item of clothing covering shoulders to waist, hips
  • A cover or lid
  • Part (e.g. road) that is the furthest away
  • Highest or upper part or point of something
  • Best or highest status or position
  • Flat upper surface or edge of an object
  • Child's toy that spins on its point
  • Upper section or leaves of fruits and vegetables
  • Winning in a sport or contest
  • verb
  • To be higher or larger than a specific value
  • To arrive at the highest point of something
  • To put a cover or layer or over something
  • To kill; murder
  • To hold the highest position on a list
  • To be more important, successful or better than
  • To beat someone or win at a game

bit

Copy vocabulary

US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

derivative

Copy vocabulary

US / dɪˈrɪvətɪv /

UK / dɪˈrɪvətɪv /

B1
  • adjecitve
  • Not from original ideas; from somewhere else

nice

Copy vocabulary

US / naɪs /

UK / naɪs /

A1
  • adjecitve
  • Being attractive or of high quality or value
  • Good or enjoyable
  • Being kind or friendly

multiply

Copy vocabulary

US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • verb
  • To increase in number by reproducing/having babies
  • To increase something by a large quantity
  • To have increased by a large quantity
  • To calculate two numbers e.g. 2 x 4

build

Copy vocabulary

US / bɪld /

UK / bɪld /

A1
  • noun
  • Your physical shape; physique
  • verb
  • To establish e.g. a reputation, over time
  • To construct a house, office, factory

work

Copy vocabulary

US / wɜ:k /

UK / wɚk /

A1
  • adjecitve
  • Activity completed in order to make money
  • noun
  • The product of some artistic or literary endeavor
  • Everything created by an author, artist, musician
  • Activity you do in order to make money
  • Place of employment
  • Final product or result of a some labor or effort
  • verb
  • To bring into a specific state of success
  • To be functioning properly, e.g. a car
  • To do your job in your company or workplace
  • To make an effort to do something
  • To operate a machine or device

introduce

Copy vocabulary

US / ˌɪntrəˈdju:s /

UK / ˌɪntrəˈdus, -ˈdjus /

A1
  • verb
  • To open an essay to set the scene
  • To guide or explain something, e.g. a town
  • To begin the use of a new thing or practice
  • To make someone known to another by name
  • To insert or put something inside another thing

approach

Copy vocabulary

US / ə'prəʊtʃ /

UK / əˈprəʊtʃ /

A2
  • noun
  • Means of reaching a place, often a road or path
  • Request of someone with a specific goal in mind
  • Specific way to handle a project, task, problem
  • verb
  • To get close to reaching something or somewhere
  • To request someone to do something specific

way

Copy vocabulary

US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

their

Copy vocabulary

US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

they

Copy vocabulary

US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

very

Copy vocabulary

US / 'verɪ /

UK / ˈvɛri /

A1
  • adjecitve
  • Concerning a large degree or amount
  • adverb
  • A lot; much; many
  • Used to stress or emphasize a noun

difference

Copy vocabulary

US / 'dɪfrəns /

UK / ˈdɪfərəns, ˈdɪfrəns /

A1
  • noun
  • A thing or issue that people do not agree about
  • Not of the same kind; unlike other things

head

Copy vocabulary

US / hed /

UK / hɛd /

A1
  • noun
  • Counter for the number of cattle
  • Natural mental ability or intelligence
  • Leader or person with the greatest authority
  • Mind; mental ability; mental state
  • Side of a coin with a head on it
  • Top part of your body with eyes and a mouth
  • Starting point of something, e.g. a river
  • verb
  • To hit a ball with your head in a game
  • To be first or at the front or top (e.g. a list)
  • To travel or move toward a particular place; To go in a particular direction
  • To become the leader of something
  • To lead or be responsible for something

exact

Copy vocabulary

US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

limit

Copy vocabulary

US / 'lɪmɪt /

UK / ˈlɪmɪt /

A2
  • noun
  • Point beyond which it is not possible to go
  • verb
  • To stop or prevent an increase past a point

well

Copy vocabulary

US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

algebraic

Copy vocabulary

US / ˌældʒɪ'breɪɪk /

UK / ˌældʒəˈbreɪk /

C1
  • adjecitve
  • Concerning algebra

foundation

Copy vocabulary

US / faunˈdeiʃən /

UK / faʊnˈdeʃən /

C1
  • noun
  • Base or important starting point
  • Underground base on which building is constructed
  • Institution supported by a private fund
  • First cosmetic used when putting on makeup
  • Action of establishing an organization

just

Copy vocabulary

US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

constant

Copy vocabulary

US / 'kɒnstənt /

UK / ˈkɑnstənt /

A2
  • adjecitve
  • Happening frequently or without pause
  • noun
  • Thing that happens always or at a regular rate

combination

Copy vocabulary

US / ˌkɒmbɪ'neɪʃn /

UK / ˌkɑmbəˈneʃən /

B1
  • noun
  • Series of letters or numbers needed to open a lock
  • Act or result of mixing things together

few

Copy vocabulary

US / fju: /

UK / fju /

A1
  • pronoun
  • Not many, a small number

positive

Copy vocabulary

US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

for

Copy vocabulary

US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

time

Copy vocabulary

US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

why

Copy vocabulary

US / waɪ /

UK / hwaɪ, waɪ /

A1
  • adverb
  • Question word to ask for a reason
  • exclamation
  • (Used to express surprise or approval)

through

Copy vocabulary

US / θru: /

UK / θru /

A2
  • adjecitve
  • having finished using or doing something
  • adverb
  • From the beginning of something until the end
  • preposition
  • Over, in, across an entire thing or place
  • Allowing you to pass between, or to
  • By a particular way or process; by the use of

unsound

Copy vocabulary

US / ˌʌnˈsaʊnd /

UK / ˌʌnˈsaʊnd /

B2
  • adjecitve
  • Being untrue; not based on facts or logic
  • Not firmly made, placed, or fixed
  • Being unwell or poorly built

business

Copy vocabulary

US / ˈbɪznəs /

UK / ˈbɪznɪs /

A1
  • noun
  • A company formed for making profit
  • Matter that has to be dealt with; task; situation
  • Activity of working to make a profit

really

Copy vocabulary

US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

would

Copy vocabulary

US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

maybe

Copy vocabulary

US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

not

Copy vocabulary

US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

our

Copy vocabulary

US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

reasonable

Copy vocabulary

US / ˈri:znəbl /

UK / ˈrizənəbəl /

A2
  • adjecitve
  • Being somewhat good, but not great
  • Fair and sensible; appropriate

themselves

Copy vocabulary

US / ðəmˈselvz /

UK / ðɛmˈsɛlvz, ðəm- /

A1
  • pronoun
  • Reflexive form of 'they'

but

Copy vocabulary

US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

good

Copy vocabulary

US / ɡʊd /

UK / ɡʊd /

A1
  • adjecitve
  • Proper, appropriate or right
  • (Of an amount) enough; plenty
  • Excellent; high quality
  • Acting well or properly; of moral character
  • In a positive or happy emotional state
  • noun
  • Advantage or benefit

give

Copy vocabulary

US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

zero

Copy vocabulary

US / ˈzɪərəʊ /

UK / ˈzɪroʊ /

A1
  • noun
  • Temperature when water turns to ice
  • number
  • Number 0
  • verb
  • To set a scale or other device to show 0

sum

Copy vocabulary

US / sʌm /

UK / sʌm /

A2
  • noun
  • Amount when all is added together; total
  • verb
  • To add two or more numbers together; total

want

Copy vocabulary

US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

can

Copy vocabulary

US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

definition

Copy vocabulary

US / ˌdefɪˈnɪʃn /

UK / ˌdɛfəˈnɪʃən /

A2
  • noun
  • Explanation of word's meaning, as in dictionaries
  • The sharpness of an image on a screen
  • Visual clearness in a photo or on a screen

equal

Copy vocabulary

US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

Copy vocabulary

US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

carry

Copy vocabulary

US / ˈkæri /

UK / ˈkæri /

A1
  • verb
  • To have a child, be pregnant
  • To have a disease you might give to others
  • (Of stores) to sell a particular product
  • To hold something and move it to another place
  • To travel a long distance (sound)
  • To support the weight or burden of something

graphical

Copy vocabulary

US / ˈgræfɪkl /

UK / ˈɡræfɪkl /

B2
  • adjecitve
  • Detailed so something is very clear

same

Copy vocabulary

US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant
  • Subtitles section
  • In the last video, we introduced you to the derivative property right over here, that if my function's equal to some constant, that the derivative is going to be zero at any x.
  • And we made a graphical argument, and we also used the definition of limits to feel good about that.
  • Now let's give a few more of these properties.
  • And these are core properties.
  • As you, throughout the rest of your calculus life, your career, you will be using some combination of these properties to find derivatives.
  • So it's good to, one, know about them, and then to feel good that they're actually true.
  • So the second one is if my function, f of x, is equal to some constant times another function, g of x, well, then the derivative of f of x is going to be equal to that same constant.
  • Let me do it.
  • That same constant times the derivative of g of x.
  • And once again, maybe we could make a, actually, we could make a graphical argument for why that is true.
  • This is going to multiply the slope, is one way to think about it.
  • But it's easier to make an algebraic argument just using, frankly, we could use either one of these definitions of the derivative.
  • I'll use the one on the right because it feels more general, although you could say, well, this is true for a, but x could be any a.
  • But I'll just use the one on the right.
  • So if we want to find f prime of x, f prime of x using this definition, we know, we know, whoops, my pen doesn't work.
  • F prime of x is going to be equal to the limit as x, sorry, as h approaches zero, I'm using that definition, of f of x plus h minus f of x, all of that over, all of that over h.
  • Well, what is f of x plus h?
  • So this is the limit as h approaches zero.
  • F of x plus h is k times g of x plus h minus f of x, well, that's just k g of x, k g of x, all of that over h.
  • And then you can factor the k out.
  • This is going to be equal to the limit as h approaches zero of k times g of x plus h minus g of x, all of that over h.
  • All I did is I factored that k out.
  • And we know from our limit properties that this is the same thing as k times the limit as h approaches zero of g of x plus h minus g of x, all of that over h.
  • And of course, all of this business right over there, that is just g prime of x.
  • So this is equal to k times g prime of x.
  • And I know what you might be thinking.
  • Well, hey, this feels like it was probably going to be true, so I just assumed it was true.
  • But you can't just assume that.
  • And I don't know, sometimes you can, when you're first trying to get your head around it, you can say, oh, this seems like a reasonable thing.
  • But in math, we like to really know that it is true.
  • Otherwise, we will build all sorts of conclusions based on unsound foundations.
  • This allows us to ensure that, look, this is something that we can do.
  • So this is, it's good to go through what might feel like a little bit of work to get to this conclusion.
  • Now let's do the third property.
  • The third property is the idea that if I have some function that's the sum or the difference of two other functions, so g of x and, let's see, I'm using h a lot, so h, let's say, I don't know, j of x,
  • I don't know, j, yeah, sure, why not, j of x.
  • You don't see a lot of j of x's out there.
  • Well then, well then, f prime of x is going to be equal to g prime of x plus j prime of x.
  • And this would also have been true if this, instead of it being a positive here, if this was a negative, or instead of addition, if this was subtraction.
  • If you had the sum or difference of two functions, then your derivative is gonna be the sum or the difference of their derivatives.
  • And once again, we can just go to the definition of f prime of x.
  • So f prime of x is going to be equal to the limit as h approaches zero of f of x plus h.
  • But what is f of x plus h?
  • Well, that's g of x plus h plus j of x plus h.
  • So that's f of x plus h minus f of x.
  • So f of x is g of x, g of x plus j of x, plus j of x.
  • Notice, this is f of x plus h minus f of x.
  • And we're gonna put all of that over h.
  • So we can put all of that, all of that over h.
  • Well, what is that equal to?
  • Well, we could just rearrange what we see on top here.
  • This is equal to the limit as h approaches zero.
  • Well, let's see.
  • All dimensions of g of x, I'm gonna put up front.
  • So g of x plus h minus g of x plus j of x plus h minus j of x.
  • And then all of that, I could write it like this, all of that over h.
  • Or I could, that's the same thing as this over h plus that over h.
  • And once again, we know from our limit properties that that is the exact same thing as the limit as h approaches zero of g of x plus h minus g of x, all of that over h, plus the limit as h approaches zero of j of x plus h minus j of x,
  • All of that over h.
  • And this right over here, that is the definition of g prime of x.
  • And this right over here is j prime, j prime of x.
  • And we're done.
  • And if this, instead of a positive, or if this was instead of addition, if this was subtraction, well then that subtraction would carry through and then instead of addition here, we would have subtraction.
  • So hopefully this makes you feel good about these properties.
  • The properties themselves are somewhat straightforward.
  • You could probably guess at them.
  • But it's nice to use the definition of our derivatives to actually feel that they are very good conclusions to make.