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 25E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 25E

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.

  df(a)dx=dfdadadx

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 .

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