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

解

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

y^{2} - 2 y x + y

解答ステップ

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

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

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

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

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