# 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 41E
To determine

## To find:The first and second differentiation of the given function

Expert Solution

Differentiating the function is f(x)

=100x9+25x41 , f(x)

=900x8+100x3

### Explanation of Solution

Given:

The function is

f(x)=10x10+5x5x

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)=10x10+5x5x...................(1)

The derivative of a function

y=f(x)y=f(x)=dydxy=f(x)=d2ydx2

Differentiating the equation (1) with respect to x

dydx=ddx(10x10+5x5x)dydx=100x9+25x41

Again Differentiating the equation with respect to x

dydx=100x9+25x41=f(x)d2ydx2=900x8+100x3=f(x)

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