What is the derivative of cot(csc(x)) ?

The derivative of cot(csc(x)) is csc^2(csc(x))cot(x)csc(x)

What is the first derivative of cot(csc(x)) ?

The first derivative of cot(csc(x)) is csc^2(csc(x))cot(x)csc(x)

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derivative of

cot (csc (x))

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

Solution steps

\frac{d}{d x} (cot (csc (x)))

Apply the chain rule:

- csc^{2} (csc (x)) \frac{d}{d x} (csc (x))

= - csc^{2} (csc (x)) \frac{d}{d x} (csc (x))

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

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

Simplify

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

What is the derivative of cot(csc(x)) ?
The derivative of cot(csc(x)) is csc^2(csc(x))cot(x)csc(x)
What is the first derivative of cot(csc(x)) ?
The first derivative of cot(csc(x)) is csc^2(csc(x))cot(x)csc(x)