What is (\partial)/(\partial x)(5z^2cot(xz)) ?

The answer to (\partial)/(\partial x)(5z^2cot(xz)) is -5z^3csc^2(zx)

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(\partial)/(\partial x)(5z^2cot(xz))

\frac{\partial}{\partial x} (5 z^{2} cot (x z))

- 5 z^{3} csc^{2} (z x)

Solution steps

\frac{\partial}{\partial x} (5 z^{2} cot (x z))

Treat

z

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 z^{2} \frac{\partial}{\partial x} (cot (x z))

Apply the chain rule:

- csc^{2} (x z) \frac{\partial}{\partial x} (x z)

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

\frac{\partial}{\partial x} (x z) = z

= 5 z^{2} (- csc^{2} (x z) z)

Simplify

5 z^{2} (- csc^{2} (x z) z) : - 5 z^{3} csc^{2} (z x)

= - 5 z^{3} csc^{2} (z x)

\int x cos (x) d x

\frac{d}{d x} (x^{2} + \frac{2000}{x})

\frac{d y}{d x} = x^{2} (y - 1)

\frac{d}{d x} (\frac{2 x}{x ^{4}})

\int_{0}^{1} ln (4 - 2 x) d x

What is (\partial)/(\partial x)(5z^2cot(xz)) ?
The answer to (\partial)/(\partial x)(5z^2cot(xz)) is -5z^3csc^2(zx)