   Chapter 11.6, Problem 51E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 43-52, use logarithmic differentiation to find d y / d x . Do not simplify the result. [HINT: See Example 4.] y = x x

To determine

To calculate: The value of dydx for function y=xx using the logarithmic differentiation.

Explanation

Given Information:

The provided function is y=xx.

Formula used:

Product rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f(x)g(x)+f(x)g(x).

The derivative of natural logarithm of x is ddxlnx=1x.

Calculation:

Consider the provided function, y=xx

Now, take natural logarithm on both sides of the function as,

lny=ln(xx)

Simplify the above expression as,

lny=ln(xx)=xlnx

Then, take ddx of both sides on the above expression,

ddx(lny)=ddx(xlnx)

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

f(x)1xx24

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

18. If \$8000 is invested at compounded continuously, find the future value after years.

Mathematical Applications for the Management, Life, and Social Sciences

For y = sin2 x + cos2 x, y = _____. a) 2 sin x 2 cos x b) 2 sin x cos x c) 4 sin x cos x d) 0

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