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 21E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 21E

The derivative of the given function is dydx=excosx[cosxxsinx] .

Explanation of Solution

Given:

The given function is y=excosx .

Calculation:

  y=excosx

Apply chain rule.

  df(a)dx=dfdadadx

Let f=ea,a=xcosx

  dydx=dda(ea)ddx(xcosx)

Apply product rule.

  (fg)=f'g+fg'

  dydx=dda(ea)[ddx(x)cosx+xddx(cosx)]

Use derivative rule.

  ddx(ex)=ex,ddx(xn)=nxn1andddx(cosx)=sinx .

  dydx=ea[cosx+x(sinx)]dydx=ea[cosxxsinx]

Substitute the value of a=xcosx .

  dydx=excosx[cosxxsinx]

Hence the derivativeof the given function is dydx=excosx[cosxxsinx] .

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