(\partial)/(\partial y)(xe^{2xy})

解

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

2 e^{2 x y} x^{2}

解答ステップ

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

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^{2 x y})

連鎖法則を適用:

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

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

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

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

簡素化

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

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