(\partial)/(\partial y)(y^2+2e^{x^2}xy)

解

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

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

解答ステップ

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

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

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

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

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