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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find the 50th derivative of y = cos 2x.

To determine

To find: The 50th derivative of y=cos2x.

Explanation

Given:

The function is y=cos2x.

Calculation:

The first derivative of y=cos2x is computed as follows,

y=ddx(y)=ddx(cos2x)=sin2x(2)=2sin2x

Thus, the first derivative of y=cos2x is y=2sin2x.

The second derivative of y is computed as follows,

y=ddx(y)=ddx(2sin2x)=2ddx(sin2x)

Simplify the terms,

y=2(dd(2x)(sin2x)d(2x)dx)=2(cos2x2)=22(cos2x)

Thus, the second derivative of y=cos2x is y=22(cos2x)

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