   Chapter 9.8, Problem 20E ### 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.Find f ( 4 ) ( x ) e if  f ( x ) = 1 / x .

To determine

To calculate: The value of f(4)(x) for the function, f(x)=1x.

Explanation

Given Information:

The provided function is f(x)=1x.

Formula used:

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

f(x)=nxn1

The derivative of a constant value, k, is

ddx(k)=0

Calculation:

Consider the provided function,

f(x)=1x=x1

In order to get f(1)(x) differentiate both sides with respect to x,

f(1)(x)=ddx((x)1)

Apply the power rule of derivatives,

f(1)(x)=1(x11)=x2

To get the value of f(2)(x), differentiate both sides of f(1)(x) with respect to x,

f(2)(x)=ddx(x2)=1ddx(x2)

Apply the power rule of derivatives,

f(2)(x)=(2x21)=2x3

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