Chapter 9.7, Problem 1CP

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# If a function has the form y = [ u ( x ) ] n , where n is a constant, we begin to find the derivative by using the_____ Rule and then use the_____ Rule to find the derivative of [ u ( x ) ] n .

To determine

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

Explanation

Consider the incomplete statement, â€˜if a function has the form y=[u(x)]nâ‹…v(x), where n is a constant, we begin to find the derivative by using the ___ Rule and then use the ___ Rule to find the derivative of [u(x)]n.â€™

Consider the provided function,

y=[u(x)]nâ‹…v(x)

Differentiate both sides with respect to x,

dydx=ddx([u(x)]nâ‹…v(x))

According to the product rule, a function, y=fâ‹…g is differentiated as,

dydx=gâ‹…ddx(f)+fâ‹…ddx(g)

Thus, to solve the derivative

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