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 27E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 27E

The derivative of the given function is dydr=1(r2+1)3 .

Explanation of Solution

Given:

The given function is y=rr2+1 .

Calculation:

  y=rr2+1

Use quotient rule.

  (fg)'=gf'fg'g2

  dydr=(r2+1)ddr(r)rddr(r2+1)(r2+1)2

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a12,a=r2+1

  dydr=(r2+1)ddr(r)r[dda(a12)ddr(r2+1)](r2+1)2

Use derivative rule ddx(xn)=nxn1 .

  dydr=(r2+1)r[(12a12)2r](r2+1)2

Substitute the value of a=r2+1 .

  dydr=(r2+1)r2r2+1(r2+1)2dydr=r2+1r2r2+1(r2+1)2dydr=1(r2+1)3

Hence the derivativeof the given function is dydr=1(r2+1)3 .

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