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

解

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

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

解答ステップ

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

y

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

\frac{\partial}{\partial x} (x^{3} y) = 3 y x^{2}

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

= 3 y x^{2} + e^{x y^{2}} y^{2}