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 13E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 13E

The derivative of the given function is dydx=3x2sin(a3+x3) .

Explanation of Solution

Given:

The given function is y=cos(a3+x3) .

Calculation:

  y=cos(a3+x3)

Apply chain rule.

  df(a)dx=dfdadadx

Let f=cosa,a=a3+x3

  dydx=dda(cosa)ddx(a3+x3)

Use derivative rule.

  ddx(xn)=nxn1,ddx(cosx)=sinx

  dydx=sina(3x2)

Substitute the value of a=a3+x3 .

  dydx=sin(a3+x3)(3x2)dydx=3x2sin(a3+x3)

Hence the derivativeof the given function is dydx=3x2sin(a3+x3) .

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!