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

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

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

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

\frac{x}{y ^{2} + x ^{2}}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x}{y ^{2} + x ^{2}}

y^{^{''}} + 18 y^{^{'}} + 97 y = 0

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

\int tan (x) - 2 sin (x) d x

\frac{d}{d x} (\frac{300}{x})

\frac{\partial}{\partial x} (x yz)

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