# Find the derivative of the given function.

### Single Variable Calculus: Concepts...

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

### 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

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.

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 .

### 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!