Prove that `d/(dx) (csc(x)) = -csc(x) cot(x)`

Textbook Question

Chapter 3, 3.3 - Problem 17 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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kspcr111 | In Training Educator

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`d/(dx) (csc(x))`

`=d/(dx) (1/sin(x))`

`= ((d/(dx) sin x)*1 - sinx * d/dx(1))/(sin^2(x))`

`= -cosx/(sin^2(x))`

`=-csc x cot(x)`

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