(\partial)/(\partial y)((z)(y^2z+yln(z)-z^2e^{xz}-3))

解

\frac{\partial}{\partial y} ((z) (y^{2} z + y ln (z) - z^{2} e^{x z} - 3))

z (2 zy + ln (z))

解答ステップ

\frac{\partial}{\partial y} ((z) (y^{2} z + y ln (z) - z^{2} e^{x z} - 3))

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} (y^{2} z + y ln (z) - z^{2} e^{x z} - 3)

和/差の法則を適用:

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

= z (\frac{\partial}{\partial y} (y^{2} z) + \frac{\partial}{\partial y} (y ln (z)) - \frac{\partial}{\partial y} (z^{2} e^{x z}) - \frac{\partial}{\partial y} (3))

\frac{\partial}{\partial y} (y^{2} z) = 2 zy

\frac{\partial}{\partial y} (y ln (z)) = ln (z)

\frac{\partial}{\partial y} (z^{2} e^{x z}) = 0

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

= z (2 zy + ln (z) - 0 - 0)

簡素化

= z (2 zy + ln (z))