(\partial}{\partial z}(\frac{x^2+z^2)/y+xyz+5xz^2)

解

\frac{\partial}{\partial z} (\frac{x ^{2} + z ^{2}}{y} + x yz + 5 x z^{2})

\frac{2 z}{y} + x y + 10 x z

解答ステップ

\frac{\partial}{\partial z} (\frac{x ^{2} + z ^{2}}{y} + x yz + 5 x z^{2})

x, y

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial z} (\frac{x ^{2} + z ^{2}}{y}) + \frac{\partial}{\partial z} (x yz) + \frac{\partial}{\partial z} (5 x z^{2})

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

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

\frac{\partial}{\partial z} (5 x z^{2}) = 10 x z

= \frac{2 z}{y} + x y + 10 x z