   Chapter 3.2, Problem 23E ### 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

# Differentiate. f ( x ) = x 2 e x x 2 + e x

To determine

To find: The differentiation of the function f(x)=x2exx2+ex.

Explanation

Given:

The function f(x)=x2exx2+ex.

Derivative rule:

(1) Quotient Rule: If f1(x) and f2(x) are both differentiable, then

ddx[f1(x)f2(x)]=f2(x)ddt[f1(x)]f1(x)ddx[f2(x)][f2x]2

(2) Product Rule: ddx[f1(x)f2(x)]=f1(x)ddx[f2(x)]+f2(x)ddx[f1(x)]

(3) Power Rule: ddx(xn)=nxn1

(4) Sum rule: ddx(f+g)=ddx(f)+ddx(g)

(5) Natural exponential function: ddx(ex)=ex

Calculation:

The derivative of the function f(x)=x2exx2+ex is f(x), which is obtained as follows.

f(x)=ddx(f(x))=ddx(x2exx2+ex)

Apply the quotient rule (1) and simplify the terms,

f(x)=[(x2+ex)ddx(x2ex)][(x2ex)(ddx(x2+ex))](x2+ex)2

Apply the sum rule (4) and simplify the terms,

f(x)=[(x2+ex)ddx(x2ex)][(x2ex)(ddx(x2)+ddx(ex))](x2+ex)2 (1)

Obtain the derivative of x2ex.

That is, compute ddx(x2ex)

### 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 516, evaluate the given quantity. log22

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Solve the inequalities for y. 4.

Mathematical Applications for the Management, Life, and Social Sciences

#### The length of the curve given by x = 3t2 + 2, y = 2t3, is:

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

#### True or False: If and , then .

Study Guide for Stewart's Multivariable Calculus, 8th 