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 3.1, Problem 42E
To determine

To find:

The first and second differentiation of the given function

Expert Solution

Answer to Problem 42E

Differentiating the function is drdx=12r12+13r23 , d2rdx2=14r3229r53

Explanation of Solution

Given:

The function is

  G(r)=r+r3

Concept used:

Definition of the differentiation:-Differentiation is the action of computing a derivative

The derivative of a function y=f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to x

Calculation:

The function

  G(r)=r+r3...................(1)

The derivative of a function

  y=f(x)y=f(x)=dydxy=f(x)=d2ydx2

Differentiating the equation (1) with respect to x

  drdx=ddx(r+r3)drdx=12r12+13r23

Again Differentiating the equation with respect to x

  drdx=12r12+13r23=f(x)d2rdx2=14r3229r53=f(x)

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