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Popular >

derivative of arcsinh(cot(x))

Solution

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

Solution

- 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)

Graph

Popular Examples

(\partial)/(\partial x)(ycos(z))

\frac{\partial}{\partial x} (y cos (z))

integral of (xarccos(x))/(sqrt(1-x^2))

\int \frac{x arccos ( x )}{1 - x ^{2}} d x

x^2y^{''}+6xy^'+6y=0

x^{2} y^{^{''}} + 6 x y^{^{'}} + 6 y = 0

integral from 1 to infinity of e^{-x}

\int_{1}^{\infty} e^{- x} d x

(\partial)/(\partial y)(y^2-cos(x)y)

\frac{\partial}{\partial y} (y^{2} - cos (x) y)

Frequently Asked Questions (FAQ)

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)