Chapter 9.6, Problem 2CP

### 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

# (a) If f ( x ) = 12 2 x 2 − 1 , find f'(x) by using the Power Rule (not the Quotient Rule).(b) If f ( x ) = x 3 − 1 3 , find f'(x) by using the Power Rule (not the Quotient Rule).

(a)

To determine

To calculate: The derivative of the function f(x)=122x21 using the power rule.

Explanation

Given Information:

The function is f(x)=122x2âˆ’1.

Formula used:

According to the power rule, if f(x)=xn, then,

fâ€²(x)=nxnâˆ’1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

gâ€²(x)=cfâ€²(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

fâ€²(x)=uâ€²(x)+vâ€²(x)

According to the product rule, if f(x)=u(x)â‹…v(x), then

fâ€²(x)=uâ€²(x)â‹…v(x)+vâ€²(x)â‹…u(x)

According to the property of differentiation, if a function is of the form y=un, where u=g(x),

dydx=nunâˆ’1dudx

Calculation:

Consider the provided function,

f(x)=122x2âˆ’1

Consider (2x2âˆ’1) to be u,

f(x)=12uâˆ’1

Differentiate both sides with respect to x,

fâ€²(x)=ddx(12uâˆ’1)

Simplify using the power rule,

(b)

To determine

To calculate: The derivative of the function f(x)=x313 using the power rule.

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