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

解

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

2 (2 x + y)

解答ステップ

\frac{\partial}{\partial x} (x (x + y) \cdot 2)

y

を定数として扱う

定数を除去:

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

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

積の法則を適用:

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

f = x, g = x + y

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

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

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

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

簡素化

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

= 2 (2 x + y)