`y = cot^2(sin( theta))` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 37 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsenviro | College Teacher | (Level 1) Educator Emeritus

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`y' = d/(d(theta))cot^2(sin(theta))`

`= 2 cot (sin(theta)) * d/(d(theta)) [cot(sin(theta))]`

`= 2cot(sin(theta))*(-csc^2(sin(theta)))*d/(d(theta)) (sin(theta))`

`= 2 cot(sin(theta))*(-csc^2(sin(theta)))*cos(theta)`

`= -2 cos(theta)*cot(sin(theta))*csc^2(sin(theta))`

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vineetchaurasia | (Level 1) eNoter

Posted on

This problem can be solved by substituting the variables with triple substitution then applying the formulas.

Detailed solution is given is image uploaded.

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