What is (\partial)/(\partial x)(y*arctan(x/z)) ?

The answer to (\partial)/(\partial x)(y*arctan(x/z)) is (yz)/(x^2+z^2)

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(\partial)/(\partial x)(y*arctan(x/z))

\frac{\partial}{\partial x} (y \cdot arctan (\frac{x}{z}))

\frac{yz}{x ^{2} + z ^{2}}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{( \frac{x}{z} ) ^{2} + 1} \frac{\partial}{\partial x} (\frac{x}{z})

= \frac{1}{( \frac{x}{z} ) ^{2} + 1} \frac{\partial}{\partial x} (\frac{x}{z})

\frac{\partial}{\partial x} (\frac{x}{z}) = \frac{1}{z}

= y \frac{1}{( \frac{x}{z} ) ^{2} + 1} \cdot \frac{1}{z}

Simplify

y \frac{1}{( \frac{x}{z} ) ^{2} + 1} \cdot \frac{1}{z} : \frac{yz}{x ^{2} + z ^{2}}

= \frac{yz}{x ^{2} + z ^{2}}

What is (\partial)/(\partial x)(y*arctan(x/z)) ?
The answer to (\partial)/(\partial x)(y*arctan(x/z)) is (yz)/(x^2+z^2)