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

解

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

in

解答ステップ

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

簡素化

in (x + 2 y + 3 z) : i (n x + 2 n y + 3 n z)

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

n, y, z

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

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

\frac{\partial}{\partial x} (2 n y) = 0

\frac{\partial}{\partial x} (3 n z) = 0

= i (n + 0 + 0)

簡素化

= in