# 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 25E
To determine

## Find the derivative of the given function.

Expert Solution

The derivative of the given function is dydx=4secx2tanx .

### Explanation of Solution

Given:

The given function is y=sec2x+tan2x .

Calculation:

y=sec2x+tan2x

Use sum rule.

(f+g)'=f'+g'

dydx=ddx(sec2x)+ddx(tan2x)

Apply chain rule.

Let f=a2,a=secx and f=a2,a=tanx

dydx=dda(a2)ddx(secx)+dda(a2)ddx(tanx)

Use derivative rule.

ddx(xn)=nxn1 , ddx(secx)=secxtanx and ddx(tanx)=sec2x

dydx=2asecxtanx+2asecx2

Substitute the value of a=secx and a=tanx .

dydx=2secxsecxtanx+2tanxsecx2dydx=2secx2tanx+2tanxsecx2dydx=4secx2tanx

Hence the derivativeof the given function is dydx=4secx2tanx .

### 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!