   Chapter 11.5, Problem 56E 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.] g ( x ) = 1 e x + e − x

To determine

To calculate: The derivative of the function g(x)=1ex+ex.

Explanation

Given Information:

The provided function is g(x)=1ex+ex.

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.

The derivative of e raised to a function is ddxeu=eududx.

The derivative of e raised to x is ddxex=ex.

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

Calculation:

Consider the provided function,

g(x)=1ex+ex

Rewrite the function as,

g(x)=1ex+ex=(ex+ex)1

Assume, ex+ex=u

Then the derivative is,

g(x)=ddxu1

Apply the chain rule to the function u1,

g(x)=(1)u11dudx=u2dudx=1u2dudx

Now, substitute u=ex+ex in the above expression,

g(x)=1(

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