   Chapter 2.5, Problem 73E

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# Find the given derivative by finding the first few derivatives and observing the pattern that occurs. D 103 cos 2 x

To determine

To find:

103th derivative of y = cos2x

Explanation

Rule of derivative used:

Chain rule: h(x) = fog(x)then h'x=f'gxg'(x)

Given: y = cos(2x)

Calculation:

We have given y = cos2x differentiating using chain rule we get:

y'=-2sin2x

y''= -22cos2x

y'''x=23sin(2x)

y''''x=24cos(2x)

Here we see that at fourth derivative, we get original function multiplied by fourth power of 2.

So, here first term is powers of 2 which goes on increasing by 1 at each step and next term will be the one of -sin2x, -cos2x,sin2xor cos(2x) depending on the remainder obtained after dividing the order of derivative by 4

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