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 17E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 17E

The derivative of the given function is dydx=ekx(1kx) .

Explanation of Solution

Given:

The given function is y=xekx .

Calculation:

  y=xekx

Apply product rule.

  (fg)=f'g+fg'

  dydx=ddx(x)ekx+xddθ(ekx)

Use derivative rule.

  ddx(xn)=nxn1 and ddx(ex)=ex

  dydx=ekxkxekxdydx=ekx(1kx)

Hence the derivativeof the given function is dydx=ekx(1kx) .

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