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How do you implicitly differentiate #3y + y^4/x^2 = 2#?

Thanks for your help!

Answer 1

Isabella Ackerman

yes

me too when it was asked elsewhere

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Answer 2

Cameron Alexander

I found: #(dy)/(dx)=(2y^4)/(3x^3+4xy^3)#

ou need to remember to derive also #y# as a function of #x#, so, for example: #y^2# derived will give you: #2y(dy)/(dx)# in your case you get: #3(dy)/(dx)+(4y^3x^2(dy)/(dx)-2xy^4)/x^4=0# #3(dy)/(dx)+4y^3/x^2(dy)/(dx)-2y^4/x^3=0# collect #(dy)/(dx)# and rearrange: #(dy)/(dx)=(2y^4/x^3)/(3+4y^3/x^2)=(2y^4)/(3x^3+4xy^3)#

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Answer 3

Christopher Agresta

To implicitly differentiate ( 3y + \frac{y^4}{x^2} = 2 ), follow these steps:

Differentiate each term with respect to (x).
Apply the chain rule when differentiating terms involving (y).
Solve for ( \frac{dy}{dx} ) after differentiating.

The result after differentiating is:

( 3\frac{dy}{dx} - 2\frac{y^4}{x^3} - \frac{4y^3}{x^2}y' = 0 )

Solve for ( \frac{dy}{dx} ) to get the implicit derivative.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.