BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.4, Problem 59E

a.

To determine

Find theexpression for F'(x) using given data.

Expert Solution

Answer to Problem 59E

The expression is F'(x)=f'(ex)ex .

Explanation of Solution

Given:

The given datais F(x)=f(ex) , f is differentiable on R .

Calculation:

  F(x)=f(ex)F'(x)=ddx[f(ex)]

Apply chain rule.

  df(a)dx=dfdadadx

  F'(x)=dd(ex)[f(ex)]ddx(ex)

Use derivative rule.

  ddx(ex)=ex

  F'(x)=f'(ex)ex

Hence theexpression is F'(x)=f'(ex)ex .

b.

To determine

Find the expression for G'(x) using given data.

Expert Solution

Answer to Problem 59E

The expression is G'(x)=ef(x)f'(x) .

Explanation of Solution

Given:

The given data is G(x)=ef(x) , f is differentiable on R .

Calculation:

  G(x)=ef(x)G'(x)=ddx[ef(x)]

Apply chain rule.

  df(a)dx=dfdadadx

  G'(x)=dd(f(x))[ef(x)]ddx[f(x)]

Use derivative rule.

  ddx(ex)=ex

  G'(x)=ef(x)f'(x)

Hence the expression is G'(x)=ef(x)f'(x) .

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