(\partial)/(\partial y)((z)(e^{xz}+xy))

解

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

z x

解答ステップ

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

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} (e^{x z} + x y)

和/差の法則を適用:

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

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

\frac{\partial}{\partial y} (e^{x z}) = 0

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

= z (0 + x)

簡素化

= z x