# The first and second differentiation of the given function

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### 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

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)

### 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!