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

Lösung

\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}}

Schritte zur Lösung

\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}}

\int sin^{5} (2 x) cos^{2} (2 x) d x

im pl i c i t \frac{d y}{d x}, y = 3 x^{5}

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