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

解

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

z

解答ステップ

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

z, y

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

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

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

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

= z (1 + 0 + 0)

簡素化

= z