# AP Calculus 1.4 Derivatives

AP Calculus 1.4 Derivatives. Which of the following best describes the quantity?

AP Calculus | Derivatives |

MPAC 4 | Connecting multiple representations |

MPAC 5 | Building notational fluency |

### Transcript

thinking thinking we're doing okay They're asking us to find

the y d x which means this is a derivatives

problem to find the derivative of this relation we typically

right Why explicitly is a function of x so it

looks like why equals something But in this case it's

really hard to isolate Why So we can find the

derivative implicitly Instead this is called implicit differentiation shockingly which

basically means the dependent variable Why has not been written

explicitly in terms of the independent variable x So we

start by applying the derivative with respect to x to

each and every term in the equation Well the first

term is three y squared times d y t ax

because we're finding the derivative of ah wai term with

respect to x All right our second term is negative

for x times Why squared all for this term we

have to use the product rule because we have two

terms multiplied by each other Recalled that the product rule

tells us that the derivative of f of x times

g of ax equals f of x times the derivative

of g of x plus the derivative of f of

x times G of x we can pull out the

minus four as a constant and we'll get x times

two why the y d x plus y squared times

d x d acts which is just one So the

second term simplifies to negative eight X y c y

t ax minus for y squared All right Third term

eleven x cube becomes thirty three x squared We'd multiply

it by d x d x here too But that's

still just one and finally the derivative of seven or

any constant ever is just zero Now it can isolate

the righty axe and move the terms without d y

d x to the other side of the equation Well

the widely axe times three y squared minus eight x

y equals four y squared minus thirty three x squared

Then we just divide by three y squared minus eight

X y to get the idea ax equals four y

squared minus thirty three x squared all over three y

squared minus eight x Y look carefully at the answers

because they all look really similar He is Our answer 00:02:34.0 --> [endTime] is in the river No