   Chapter 11.1, 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 each of Problems 13-18, find the derivative of the function in part (a). Then find the derivative of the function in part (b) or show that the function in part (b) is the same function as that in part (a).(a) y = ln ( x 4 − 1 ) 3 (b) y = ln ( x 4 − 1 ) 3

(a)

To determine

To calculate: The derivative of the function y=3ln(x41).

Explanation

Given Information:

The function is y=3ln(x41).

Formula Used:

Derivative of logarithmic function,

ddx(lnx)=1x

Power rule of differentiation,

ddx(xn)=nxn1

Chain rule of differentiation,

ddxf(g(x))=f(g(x))g(x)

Calculation:

Consider the given function y=3ln(x41).

By chain rule,

ddxf(g(x))=fg(x)g(x)

Apply the chain rule on the given function to get,

y=ddx(3ln(x41))=3ddx(ln

(b)

To determine

To calculate: The derivative of the function y=ln(x41)3.

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