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 30E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 30E

The derivative of the given function is f'(t)=4t22t(t2+4)32 .

Explanation of Solution

Given:

The given function is f(t)=tt2+4 .

Calculation:

  f(t)=tt2+4=(tt2+4)12

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a12,a=tt2+4

  ddtf(t)=dda(a12)ddt(tt2+4)

Use quotient rule.

  (fg)'=gf'fg'g2

  f'(t)=dda(a12)(t2+4)ddt(t)tddt(t2+4)(t2+4)2

Use derivative rule ddx(xn)=nxn1 .

  f'(t)=12a(t2+4)t(2t)(t2+4)2f'(t)=12a(t2+42t2)(t2+4)2f'(t)=12a(4t2)(t2+4)2

Substitute the value of a=tt2+4 .

  f'(t)=12tt2+4(4t2)(t2+4)2f'(t)=4t22t(t2+4)32

Hence the derivativeof the given function is f'(t)=4t22t(t2+4)32 .

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!