(\partial)/(\partial x)((z)(3x+5xy-2y^2))

解

\frac{\partial}{\partial x} ((z) (3 x + 5 x y - 2 y^{2}))

z (5 y + 3)

解答ステップ

\frac{\partial}{\partial x} ((z) (3 x + 5 x y - 2 y^{2}))

z, y

を定数として扱う

定数を除去:

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

= z \frac{\partial}{\partial x} (3 x + 5 x y - 2 y^{2})

和/差の法則を適用:

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

= z (\frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (5 x y) - \frac{\partial}{\partial x} (2 y^{2}))

\frac{\partial}{\partial x} (3 x) = 3

\frac{\partial}{\partial x} (5 x y) = 5 y

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

= z (3 + 5 y - 0)

簡素化

= z (5 y + 3)