   Chapter 11.5, Problem 60E 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 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f ( x ) = e − x x e x

To determine

To calculate: The derivative of the function f(x)=exxex.

Explanation

Given Information:

The provided function is f(x)=exxex.

Formula used:

The derivative of function f(x)=un using the chain rule is f(x)=ddx(un)=nun1dudx, where u is the function of x.

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 e raised to a function is ddxeu=eududx.

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

Calculation:

Consider the provided function,

f(x)=exxex

Rewrite the function as,

f(x)=exxex=1xexex=1xe2x=(xe2x)1

Assume, xe2x=u

Then the derivative is,

f(x)=ddxu1

Apply the chain rule to the function u1,

f(x)=(1)u11dudx=u2dudx=1u2dudx

Now, substitute u=(xe2x) in the above expression,

f(x)=1(xe2x)2ddx(xe2x

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