(\partial)/(\partial x)(x^3-5x^2y+7xy^3)

解

\frac{\partial}{\partial x} (x^{3} - 5 x^{2} y + 7 x y^{3})

3 x^{2} - 10 y x + 7 y^{3}

解答ステップ

\frac{\partial}{\partial x} (x^{3} - 5 x^{2} y + 7 x y^{3})

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}) - \frac{\partial}{\partial x} (5 x^{2} y) + \frac{\partial}{\partial x} (7 x y^{3})

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

\frac{\partial}{\partial x} (5 x^{2} y) = 10 y x

\frac{\partial}{\partial x} (7 x y^{3}) = 7 y^{3}

= 3 x^{2} - 10 y x + 7 y^{3}