What is (\partial)/(\partial y)(x^2y+(xe^x)/(y^3)) ?

The answer to (\partial)/(\partial y)(x^2y+(xe^x)/(y^3)) is x^2-(3xe^x)/(y^4)

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(\partial)/(\partial y)(x^2y+(xe^x)/(y^3))

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

x^{2} - \frac{3 x e ^{x}}{y ^{4}}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial y} (\frac{x e ^{x}}{y ^{3}}) = - \frac{3 x e ^{x}}{y ^{4}}

= x^{2} - \frac{3 x e ^{x}}{y ^{4}}

2 x^{2} - 2 x - 6, - 2, 2

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What is (\partial)/(\partial y)(x^2y+(xe^x)/(y^3)) ?
The answer to (\partial)/(\partial y)(x^2y+(xe^x)/(y^3)) is x^2-(3xe^x)/(y^4)