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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Differentiating Logarithmic Functions In Exercises 85–98, find the derivative of the function.

y = ln x 3 + 1 3

To determine

To calculate: The derivative of the function y=ln(x3+13).

Explanation

Given information:

The provided function is y=ln(x3+13).

Formula used:

The property of logarithms for the expression lnxn is lnxn=nlnx where x and y are real numbers greater than 0.

Constant multiple rule of derivative of function f(x) is f'(cx)=cf'(x) where c is constant.

The derivative of natural logarithm of a function is ddxlnu=1ududx, where u is a differentiable function of x.

Calculation:

Consider the function, y=ln(x3+13).

Rewrite the function as,

y=ln(x3+1)13

Now, apply the property of lnxn as,

y=13ln(x3+1)

Then, the derivative of the function is,

y=ddx(13ln(x3+1))

Now, apply the constant multiple rule as,

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