What is (\partial ^2)/(\partial x^2)(arctan(y/x)) ?

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

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(\partial ^2)/(\partial x^2)(arctan(y/x))

\frac{\partial ^{2}}{\partial x ^{2}} (arctan (\frac{y}{x}))

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

Solution steps

\frac{\partial ^{2}}{\partial x ^{2}} (arctan (\frac{y}{x}))

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

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

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

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

\int \frac{x ^{2} - 1}{x} d x

x \to 2 lim (\frac{1}{x ( x ^{2} - 2 )})

\frac{d y}{d x} = \frac{2 x y}{x ^{2} - y ^{2}}, y (1) = 1

\frac{6}{( s ^{3} - 2 ) ^{3}}

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

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