# Find the given derivativeby the help of pattern that occurs.

### 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 3.3, Problem 39E
To determine

## Find the given derivativeby the help of pattern that occurs.

Expert Solution

The value of the given derivative f99(x)=cosx .

### Explanation of Solution

Given:

The given derivativeis d99dx99(sinx) .

Calculation:

f(x)=sinx

f1(x)=ddx(sinx)=cosxf2(x)=ddx(cosx)=sinxf3(x)=ddx(sinx)=cosxf4(x)=ddx(cosx)=(sinx)=sinxf5(x)=ddx(sinx)=cosxf6(x)=ddx(cosx)=sinxf7(x)=ddx(sinx)=cosxf8(x)=ddx(cosx)=(sinx)=sinx

From the above pattern, the cycle is repeat itself after four derivatives.

f96(x)=sinxf97(x)=cosxf98(x)=sinxf99(x)=cosx

Hence thevalue of the given derivative f99(x)=cosx .

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