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

The answer to (\partial)/(\partial z)(arctan(x/z)) is -x/(x^2+z^2)

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

- 2 x^{2} + 50 x + 25.247

\frac{d}{d x} (x^{3} + 10)

\int \frac{ln ( x + 1 )}{( x + 1 ) ^{3}} d x

y^{^{'}} = (x + 1) \cdot (y + 1)

x \to π lim (tan (\frac{5}{6} x))

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