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Thank you We sneak all right Put this problem in

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your calculator in shmoop All right Which of the following

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best describes the quantity d y t ax given the

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relation why cubed minus four x y squared plus eleven

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x cubed equals seven and hear the potential All right

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

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the y d x which means this is a derivatives

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problem to find the derivative of this relation we typically

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right Why explicitly is a function of x so it

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

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really hard to isolate Why So we can find the

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derivative implicitly Instead this is called implicit differentiation shockingly which

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basically means the dependent variable Why has not been written

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explicitly in terms of the independent variable x So we

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start by applying the derivative with respect to x to

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each and every term in the equation Well the first

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term is three y squared times d y t ax

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

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respect to x All right our second term is negative

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for x times Why squared all for this term we

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have to use the product rule because we have two

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terms multiplied by each other Recalled that the product rule

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tells us that the derivative of f of x times

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g of ax equals f of x times the derivative

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of g of x plus the derivative of f of

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x times G of x we can pull out the

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

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two why the y d x plus y squared times

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d x d acts which is just one So the

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second term simplifies to negative eight X y c y

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t ax minus for y squared All right Third term

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

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

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still just one and finally the derivative of seven or

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any constant ever is just zero Now it can isolate

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the righty axe and move the terms without d y

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d x to the other side of the equation Well

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the widely axe times three y squared minus eight x

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y equals four y squared minus thirty three x squared

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Then we just divide by three y squared minus eight

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X y to get the idea ax equals four y

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squared minus thirty three x squared all over three y

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squared minus eight x Y look carefully at the answers

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

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