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 14E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 14E

The derivative of the given function is dydx=3sinxcos2x .

Explanation of Solution

Given:

The given function is y=a3+cos3x .

Calculation:

  y=a3+cos3x

Apply sum rule.

  (f+g)=f'+g'

  dydx=ddx(a3)+ddx(cos3x)dydx=0+ddx(cos3x)dydx=ddx(cos3x)

Apply chain rule.

  df(a)dx=dfdadadx

Let f=u3,u=cosx

  dydx=ddu(u3)ddx(cosx)

Use derivative rule.

  ddx(cosx)=sinx

  dydx=3u2(sinx)dydx=3u2sinx

Substitute the value of u=cosx .

  dydx=3cos2xsinxdydx=3sinxcos2x

Hence the derivativeof the given function is dydx=3sinxcos2x .

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