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

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

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

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

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

Solution steps

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

Treat

z

as a constant

Take the constant out:

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

= 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

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

Simplify

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

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

\frac{\partial}{\partial y} (8 x cos (3 x y))

\int \frac{( 6 x ^{2} + 7 x - 6 )}{( x ^{2} - 4 ) ( x + 2 )} d x

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

\int_{0}^{4} 4 - x^{2} d x

\frac{d x}{d t} - 3 x = t

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