(\partial)/(\partial y)((xe^y)^2)

解

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

x^{2} e^{2 y} \cdot 2

解答ステップ

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

簡素化

(x e^{y})^{2} : e^{2 y} x^{2}

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

x

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

e^{2 y} \frac{\partial}{\partial y} (2 y)

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

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

= x^{2} e^{2 y} \cdot 2