(\partial)/(\partial y)(xe^{y/x})

解

\frac{\partial}{\partial y} (x e^{\frac{y}{x}})

e^{\frac{y}{x}}

解答ステップ

\frac{\partial}{\partial y} (x e^{\frac{y}{x}})

x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

連鎖法則を適用:

e^{\frac{y}{x}} \frac{\partial}{\partial y} (\frac{y}{x})

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

\frac{\partial}{\partial y} (\frac{y}{x}) = \frac{1}{x}

= x e^{\frac{y}{x}} \frac{1}{x}

簡素化

x e^{\frac{y}{x}} \frac{1}{x} : e^{\frac{y}{x}}

= e^{\frac{y}{x}}