   Chapter 9.8, Problem 16E ### 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

# In Problems 13-24, find the indicated derivative.If f ( x ) = x − 5 , find  f ' " ( x ) .

To determine

To calculate: The value of f(x) for the function, f(x)=x5.

Explanation

Given Information:

The provided function is f(x)=x5.

Formula used:

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

f(x)=nxn1

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

g(x)=cf(x)

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

f(x)=u(x)+v(x)

The derivative of a constant value, k, is

ddx(k)=0

According to the chain rule of derivatives, for a function y=[u(x)]n, the derivative of y is equal to

dydx=n[u(x)]n1(u(x))

Calculation:

Consider the provided function,

f(x)=x5=(x5)12

In order to get f(x) differentiate both sides with respect to x,

f(x)=ddx((x5)12)

Apply the chain rule of derivatives,

f(x)=12(x5)121(ddx(x5))=12(x5)12(ddx(x)ddx(5))=12(x5)12(x110)=12(x5)12

To find the value of f(x), differentiate both sides of f(x) with respect to x,

f(x)=ddx(12(x5)12)

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