   Chapter 2.5, Problem 86E

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# Suppose y = f ( x ) is a curve that always lies above the x-axis and never has a horizontal tangent, where f is differentiable everywhere. For what value of y is the rate of change of y 5 with respect to x eighty times the rate of change of y with respect to x?

To determine

To Find:

Value of y for which the rate of change of y5 with respect to x is eighty times the rate of change of y with respect to x.

Explanation

Rule used:

Chain rule:

ddxfogx=f'gxg'(x)

Given:

ddxy5=80 dydx

Calculation:

By using chain rule:

5y4dydx=

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