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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

in v erse l a pl a ce \frac{2}{s ^{2} + 2 s + 2}

\int \frac{3}{2} x^{2} - 3 x^{4} d x

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

\frac{d}{d x} (8 x^{5} + 45 x^{4} + 80 x^{3} + 50 x^{2} + 200)

d er i v a t i v e e^{t} cos (t)