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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

\int - 2 x + 9 x^{2} - 4 x^{3} + 14 d x

d er i v a t i v e 10 e^{x^{2}} x

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

\int \frac{1}{sin ^{2} ( x ) + 1} d x

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