   Chapter 3.3, Problem 51E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the given derivative by finding the first few derivatives and observing the pattern that occurs. d 99 d x 99 ( sin x )

To determine

To find: The derivative of d99dx99(sinx).

Explanation

Let f(x)=sinx, then d99dx99(f(x))=d99dx99(sinx).

The first derivative of f(x) is computed as follows,

ddx(f(x))=ddx(sinx)=cosx

Thus, the first derivative of f(x) is ddx(f(x))=cosx (1)

The second derivative of f(x) is computed as follows,

d2dx2(f(x))=ddx(ddx(f(x)))=ddx(cosx)            [by(1)]=sinx

Thus, the second derivative of f(x) is d2dx2(f(x))=sinx (2)

The third derivative of f(x) is computed as follows,

d3dx3(f(x))=ddx(d2dx2(f(x)))=ddx(sinx)            [by(2)]=ddx(sinx)=cosx

Thus, the third derivative of f(x) is d3dx3(f(x))=cosx<

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