(\partial)/(\partial x)((y)(8-4x^2-2z^2))

解

\frac{\partial}{\partial x} ((y) (8 - 4 x^{2} - 2 z^{2}))

- 8 y x

解答ステップ

\frac{\partial}{\partial x} ((y) (8 - 4 x^{2} - 2 z^{2}))

y, z

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

\frac{\partial}{\partial x} (8) = 0

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

\frac{\partial}{\partial x} (2 z^{2}) = 0

= y (0 - 8 x - 0)

簡素化

= - 8 y x