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

The derivative of arcsinh(cot(x)) is -csc(x)

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

The first derivative of arcsinh(cot(x)) is -csc(x)

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

- csc (x)

Solution steps

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

Apply the chain rule:

\frac{1}{( cot ( x ) ) ^{2} + 1} \frac{d}{d x} (cot (x))

= \frac{1}{( cot ( x ) ) ^{2} + 1} \frac{d}{d x} (cot (x))

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

= \frac{1}{( cot ( x ) ) ^{2} + 1} (- csc^{2} (x))

Simplify

\frac{1}{cot ^{2} ( x ) + 1} (- csc^{2} (x)) : - csc (x)

= - csc (x)

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