(\partial)/(\partial y)((z)(x+2y+3z))

解

\frac{\partial}{\partial y} ((z) (x + 2 y + 3 z))

2 z

解答ステップ

\frac{\partial}{\partial y} ((z) (x + 2 y + 3 z))

z, x

を定数として扱う

定数を除去:

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

= z \frac{\partial}{\partial y} (x + 2 y + 3 z)

和/差の法則を適用:

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

= z (\frac{\partial}{\partial y} (x) + \frac{\partial}{\partial y} (2 y) + \frac{\partial}{\partial y} (3 z))

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

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

\frac{\partial}{\partial y} (3 z) = 0

= z (0 + 2 + 0)

簡素化

= 2 z