(\partial)/(\partial x)((u)(3x(x-1)))

解

\frac{\partial}{\partial x} ((u) (3 x (x - 1)))

3 u (2 x - 1)

解答ステップ

\frac{\partial}{\partial x} ((u) (3 x (x - 1)))

u

を定数として扱う

定数を除去:

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

= u \cdot 3 \frac{\partial}{\partial x} (x (x - 1))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x - 1

= u \cdot 3 (\frac{\partial}{\partial x} (x) (x - 1) + \frac{\partial}{\partial x} (x - 1) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x - 1) = 1

= u \cdot 3 (1 \cdot (x - 1) + 1 \cdot x)

簡素化

u \cdot 3 (1 \cdot (x - 1) + 1 \cdot x) : 3 u (2 x - 1)

= 3 u (2 x - 1)