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

解

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

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

解答ステップ

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

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^{x y^{2}})

連鎖法則を適用:

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

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

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

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

簡素化

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

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