# The 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 44E
To determine

## To find:The differentiation of the given function

Expert Solution

Differentiating the function is f(x)

=ex3x2 , f(x)=ex6x

### Explanation of Solution

Given:

The function is

f(x)=exx3

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

f(x)=exx3..................(1)

The derivative of a function

y=f(x)y=f(x)=dydx

Differentiating the equation (1) with respect to x

f(x)=dydx=ddx(exx3)dydx=ddx(ex)ddx(x3)f(x)=ex3x2

Again Differentiating the above equation with respect to x

f(x)=ex3x2f(x)=d2ydx2=ddx(ex3x2)f(x)=ex6x

Draw the table

f(x)=2x5x34

Test one point in each of the region formed by the graph

If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function

 x−axis 0 −0.4 1.87 4.5 y−axis 1 0.74 0 0

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