What is the (csc^2(x))^' ?

The (csc^2(x))^' is -2csc^2(x)cot(x)

What is the first (csc^2(x))^' ?

The first (csc^2(x))^' is -2csc^2(x)cot(x)

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(csc^{2} (x))^{^{'}}

- 2 csc^{2} (x) cot (x)

Solution steps

(csc^{2} (x))^{'}

Apply the chain rule:

2 csc (x) (csc (x))^{'}

= 2 csc (x) (csc (x))^{'}

(csc (x))^{'} = - cot (x) csc (x)

= 2 csc (x) (- cot (x) csc (x))

Simplify

2 csc (x) (- cot (x) csc (x)) : - 2 csc^{2} (x) cot (x)

= - 2 csc^{2} (x) cot (x)

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