(\partial)/(\partial x)((y)(y^3+x^3-6xy))

解

\frac{\partial}{\partial x} ((y) (y^{3} + x^{3} - 6 x y))

y (3 x^{2} - 6 y)

解答ステップ

\frac{\partial}{\partial x} ((y) (y^{3} + x^{3} - 6 x y))

y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (y^{3} + x^{3} - 6 x y)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= y (\frac{\partial}{\partial x} (y^{3}) + \frac{\partial}{\partial x} (x^{3}) - \frac{\partial}{\partial x} (6 x y))

\frac{\partial}{\partial x} (y^{3}) = 0

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

\frac{\partial}{\partial x} (6 x y) = 6 y

= y (0 + 3 x^{2} - 6 y)

簡素化

= y (3 x^{2} - 6 y)