   Chapter 9.7, Problem 2CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# If a function has the form y = [ ( x ) / v ( x ) ] ”, where n is a constant, we begin to find the derivative by using the______ Rule and then use the_________ Rule.

To determine

To fill: The incomplete statement, ‘if a function has the form y=[u(x)v(x)]n, where n is a constant, we begin to find the derivative by using the ___ Rule and then use the ___ Rule.’

Explanation

Consider the incomplete statement, ‘if a function has the form y=[u(x)v(x)]n, where n is a constant, we begin to find the derivative by using the ___ Rule and then use the ___ Rule.’

Consider the provided function,

y=[u(x)v(x)]n

Differentiate both sides with respect to x,

dydx=ddx([u(x)v(x)]n)

According to the power rule, for a function, y=xn,

dydx=nxn1

Thus, to solve the derivative of y, first the power rule will be applied,

dydx=<

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