`f(x) = cot(x)` Find the second derivative of the function.

Textbook Question

Chapter 2, Review - Problem 73 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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Note:- 1) If y = cotx ; then dy/dx = `-cosec^2(x)`

` `

2) If y = cosecx ; then dy/dx = -cosecx*cotx

Now,

`f(x) = y = cotx`

differentiating 

`f'(x) = y' = -cosec^2(x)`

differentiating

`f''(x) = 2cosecx*cosecx*cotx`

or, `f''(x) = y'' = 2cotx*cosec^2x`

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