(\partial)/(\partial u)((x)(-3u-3v^2))

解

\frac{\partial}{\partial u} ((x) (- 3 u - 3 v^{2}))

- 3 x

解答ステップ

\frac{\partial}{\partial u} ((x) (- 3 u - 3 v^{2}))

x, v

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

\frac{\partial}{\partial u} (3 u) = 3

\frac{\partial}{\partial u} (3 v^{2}) = 0

= x (- 3 - 0)

簡素化

= - 3 x