(\partial)/(\partial x)(x(x-2y))

解

\frac{\partial}{\partial x} (x (x - 2 y))

2 x - 2 y

解答ステップ

\frac{\partial}{\partial x} (x (x - 2 y))

y

を定数として扱う

積の法則を適用:

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

f = x, g = x - 2 y

= \frac{\partial}{\partial x} (x) (x - 2 y) + \frac{\partial}{\partial x} (x - 2 y) x

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

\frac{\partial}{\partial x} (x - 2 y) = 1

= 1 \cdot (x - 2 y) + 1 \cdot x

簡素化

1 \cdot (x - 2 y) + 1 \cdot x : 2 x - 2 y

= 2 x - 2 y