(\partial)/(\partial y)((z)(8xyz-e^z))

解

\frac{\partial}{\partial y} ((z) (8 x yz - e^{z}))

8 z^{2} x

解答ステップ

\frac{\partial}{\partial y} ((z) (8 x yz - e^{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} (8 x yz - e^{z})

和/差の法則を適用:

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

= z (\frac{\partial}{\partial y} (8 x yz) - \frac{\partial}{\partial y} (e^{z}))

\frac{\partial}{\partial y} (8 x yz) = 8 z x

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

= z (8 z x - 0)

簡素化

z (8 z x - 0) : 8 z^{2} x

= 8 z^{2} x