(\partial)/(\partial x)(xy^2-x^3y)

解

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

y^{2} - 3 y x^{2}

解答ステップ

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

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

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

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

= y^{2} - 3 y x^{2}