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 12E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 12E

The derivative of the given function is f'(t)=sec2t3(1+tant)23 .

Explanation of Solution

Given:

The given function is f(t)=1+tant3 .

Calculation:

  f(t)=1+tant3=(1+tant)13

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a13,a=1+tant

  ddtf(t)=dda(a13)ddt(1+tant)

Use derivative rule.

  ddx(xn)=nxn1,ddx(tanx)=sec2x

  f'(t)=13a23(0+sec2t)f'(t)=sec2t3a23

Substitute the value of a=1+tant .

  f'(t)=sec2t3(1+tant)23

Hence the derivativeof the given function is f'(t)=sec2t3(1+tant)23 .

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