(\partial)/(\partial y)(e^{xy^2}+4zy^3)

解

\frac{\partial}{\partial y} (e^{x y^{2}} + 4 z y^{3})

e^{x y^{2}} \cdot 2 x y + 12 z y^{2}

解答ステップ

\frac{\partial}{\partial y} (e^{x y^{2}} + 4 z y^{3})

x, z

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} (e^{x y^{2}}) + \frac{\partial}{\partial y} (4 z y^{3})

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

\frac{\partial}{\partial y} (4 z y^{3}) = 12 z y^{2}

= e^{x y^{2}} \cdot 2 x y + 12 z y^{2}