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

解

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

y^{2} - 2 x y + 1

解答ステップ

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

\frac{\partial}{\partial x} (x) = 1

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

\frac{\partial}{\partial x} (y) = 0

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

= 1 - 2 y x - 0 + y^{2}

簡素化

= y^{2} - 2 x y + 1