   Chapter 4.5, Problem 2CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Find the derivative of each function. f ( x ) = ln ( x 2 − 4 ) b. f ( x ) = x 2 ln x c. f ( x ) = − ln x x 2

(a)

To determine

To calculate: The derivative of the function f(x)=ln(x24).

Explanation

Given information:

The provided function is f(x)=ln(x24).

Formula used:

The chain rule of derivative for natural logarithm

ddxlnu=1ududx.

Where, u is the function of x.

The chain rule of derivative for power function:

ddx(un)=nun1dudx

Where, u is the function of x.

The power rule of derivative:

ddxxn=xn1

Calculation:

Consider the function

f(x)=ln(x24),

Let u=(x24),

Now differentiate the function with respect to x,

dudx=ddx(x24)=2x0<

(b)

To determine

To calculate: The derivative of the function f(x)=x2lnx.

(c)

To determine

To calculate: The derivative of the function f(x)=lnxx2.

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