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 3.3, Problem 39E
To determine

Find the given derivativeby the help of pattern that occurs.

Expert Solution

Answer to Problem 39E

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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