   Chapter 3.6, Problem 41E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Use logarithmic differentiation to find the derivative of the function. y = x − 1 x 4 + 1

To determine

To find: The derivative of y by using logarithmic differentiation.

Explanation

Given:

The function is y=x1x4+1.

Result used: Chain Rule

If y=f(u) and u=g(x) are both differentiable functions, then dydx=dydududx.

Calculation:

Consider y=x1x4+1,

Take natural logarithm on both sides,

lny=ln[(x1)12(x4+1)12]lny=ln(x1)12ln(x4+1)12      (Qlnab=lnalnb)lny=12ln(x1)12ln(x4+1)    (Qlnxa=alnx)

Differentiate both sides with respect to x.

ddx(lny)=ddx(12ln(x1)12ln(x4+1))ddx(lny)=ddx(12ln(x1))ddx(12ln(x4+1))

Let u=x1 and v=x4+1

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 4144, determine whether the statement is true or false. 44. 561112

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 23-58, perform the indicated operations and simplify. 54.

Mathematical Applications for the Management, Life, and Social Sciences

#### The graph at the right is the direction field for: a) y = x y b) y = xy c) y = x + y d) y = xy

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 