# The prove that the derivative of an even function is an odd 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 2.7, Problem 53E

(a)

To determine

## To find: The prove that the derivative of an even function is an odd function.

Expert Solution

### Explanation of Solution

Given information:

The even function f(x) is given.

Differentiate the function f(x) ,

f(x)=limh0f(x+h)f(x)h=limh0f[(x+h)]f(x)(h)=limh0f[(x+h)]f(x)(h)=f(x)

Hence, the derivative of an even function is an odd function.

(b)

To determine

Expert Solution

### Explanation of Solution

Given information:

The odd function f(x) is given.

Differentiate the function f(x) ,

f(x)=limh0f[(x+h)]f(x)h=limh0f[(xh)]f(x)h=f(x)

Hence, the derivative of an odd function is an even function.

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