# 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 45E

(A)

To determine

## To show:The differentiation of the given function

Expert Solution

d2ydx2=3t

### Explanation of Solution

Given:

The equation of motion of a particle is

s=t33t

Where f and g have derivatives of all orders

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

s=t33t...................(1)

The derivative of a function

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

Differentiating the equation (1) with respect to x

s=dydx=ddx(t33t)s=3t23

Again Differentiating the above equation with respect to x

d2ydx2=ddx(3t23)d2ydx2=3t

(B)

To determine

Expert Solution

d2ydx2=6

### Explanation of Solution

Given:

The equation of motion of a particle is

s=t33t

Where f and g have derivatives of all orders

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

s=t33t...................(1)

The derivative of a function

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

Differentiating the equation (1) with respect to x

s=dydx=ddx(t33t)s=3t23

Again Differentiating the above equation with respect to x

d2ydx2=ddx(3t23)d2ydx2=3t

Putting the t=2

d2ydx2=3td2ydx2=3×2d2ydx2=6

(C)

To determine

Expert Solution

dydx=3

### Explanation of Solution

Given:

The equation of motion of a particle is

s=t33t

Where f and g have derivatives of all orders

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

s=t33t...................(1)

The derivative of a function

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

Differentiating the equation (1) with respect to x

s=dydx=ddx(t33t)s=3t23

Putting the s=0

s=3t23s=3

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