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

解

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

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

解答ステップ

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

x

を定数として扱う

和/差の法則を適用:

(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}}