   Chapter 4.5, Problem 3CP ### 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
1 views

# Find the derivative of f ( x ) = ln x + 1 3 .

To determine

To calculate: The derivative of the function f(x)=ln(x+13).

Explanation

Given information:

The provided function is f(x)=ln(x+13).

Formula used:

The chain rule of derivative for natural logarithm

ddxlnu=1ududx.

Where, u is the function of x.

The property of logarithms,

lnxa=alnx

Calculation:

Consider the function

f(x)=ln(x+13)=ln(x+1)1/3.

Apply the property of logarithms,

ln(x+1)1/3=ln(x+1)13=13ln(x+1)

Let u=x+1,

Now differentiate the function with respect to x,

dudx=ddx(x+1)=1

Substitute, u for x+1 in function,

f(x)=13lnu

Now differentiate the function with respect to x

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