What is (\partial)/(\partial x)(3z^3cot(xz)) ?

The answer to (\partial)/(\partial x)(3z^3cot(xz)) is -3z^4csc^2(zx)

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(\partial)/(\partial x)(3z^3cot(xz))

\frac{\partial}{\partial x} (3 z^{3} cot (x z))

- 3 z^{4} csc^{2} (z x)

Solution steps

\frac{\partial}{\partial x} (3 z^{3} cot (x z))

Treat

z

as a constant

Take the constant out:

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

= 3 z^{3} \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

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

Simplify

3 z^{3} (- csc^{2} (x z) z) : - 3 z^{4} csc^{2} (z x)

= - 3 z^{4} csc^{2} (z x)

\frac{\partial}{\partial x} (3 x + x y + x^{2} y - 2 y)

\frac{\partial}{\partial x} (\frac{1}{∣ x ∣})

\int_{0}^{2} 2 x + 5 d x

\frac{d}{d x} (40 x (5 x^{2} - 8))

What is (\partial)/(\partial x)(3z^3cot(xz)) ?
The answer to (\partial)/(\partial x)(3z^3cot(xz)) is -3z^4csc^2(zx)