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 44E
To determine

To find:

The differentiation of the given function

Expert Solution

Answer to Problem 44E

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

    xaxis 0 0.4 1.87 4.5
    yaxis 1 0.74 0 0

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 3.1, Problem 44E

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