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Find dy/dx by implicit differentiation and evaluate the derivative at the given point.

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Find dy/dx by implicit differentiation and evaluate the derivative at the given point.

x^2/3 + y^2/3 = 5,   (8, 1)
asked Jan 22, 2015 in CALCULUS by anonymous

1 Answer

0 votes

Step 1:

The function is and point is .

Apply derivative on each side with respect to .

Use sum rule : .

image

Use power rule : image.

image

image

Take out common factor image and simplify it.

image

image

image

image

image

image

image.

Step 2:

The point is .

Substitute image in image.

image

image.

Solution :

image.

image.

answered Jan 22, 2015 by joseph Apprentice
edited Jan 22, 2015 by joseph
ln(y)=2y^2-x; (2,1)

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