(\partial)/(\partial x)((z)(2x^3-4x^2-6y))

解

\frac{\partial}{\partial x} ((z) (2 x^{3} - 4 x^{2} - 6 y))

z (6 x^{2} - 8 x)

解答ステップ

\frac{\partial}{\partial x} ((z) (2 x^{3} - 4 x^{2} - 6 y))

z, y

を定数として扱う

定数を除去:

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

= z \frac{\partial}{\partial x} (2 x^{3} - 4 x^{2} - 6 y)

和/差の法則を適用:

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

= z (\frac{\partial}{\partial x} (2 x^{3}) - \frac{\partial}{\partial x} (4 x^{2}) - \frac{\partial}{\partial x} (6 y))

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

\frac{\partial}{\partial x} (6 y) = 0

= z (6 x^{2} - 8 x - 0)

簡素化

= z (6 x^{2} - 8 x)