Question

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

x^2/3 + y^2/3 = 5,   (8, 1)

Answer 1

Step 1:

The function is and point is .

Apply derivative on each side with respect to .

Use sum rule : .

Use power rule : .

Take out common factor and simplify it.

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Step 2:

The point is .

Substitute in .

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Solution :

.

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