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

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

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

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

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

Solution steps

\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}}

\frac{2}{s ^{2} + 2 s + 2}

- x^{2} + x + a

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

e^{t} cos (t)

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