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

The answer to (\partial ^2)/(\partial y^2)(x/(x^2+y^2)) is -(2x(x^2-3y^2))/((x^2+y^2)^3)

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

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

- \frac{2 x ( x ^{2} - 3 y ^{2} )}{( x ^{2} + y ^{2} ) ^{3}}

Solution steps

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

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

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

\frac{\partial}{\partial y} (- \frac{2 x y}{( x ^{2} + y ^{2} ) ^{2}}) = - \frac{2 x ( x ^{2} - 3 y ^{2} )}{( x ^{2} + y ^{2} ) ^{3}}

= - \frac{2 x ( x ^{2} - 3 y ^{2} )}{( x ^{2} + y ^{2} ) ^{3}}

What is (\partial ^2)/(\partial y^2)(x/(x^2+y^2)) ?
The answer to (\partial ^2)/(\partial y^2)(x/(x^2+y^2)) is -(2x(x^2-3y^2))/((x^2+y^2)^3)