(\partial)/(\partial x)(5-3x+6y-2x^2y)

解

\frac{\partial}{\partial x} (5 - 3 x + 6 y - 2 x^{2} y)

- 4 x y - 3

解答ステップ

\frac{\partial}{\partial x} (5 - 3 x + 6 y - 2 x^{2} y)

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 x} (5) - \frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (6 y) - \frac{\partial}{\partial x} (2 x^{2} y)

\frac{\partial}{\partial x} (5) = 0

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

\frac{\partial}{\partial x} (6 y) = 0

\frac{\partial}{\partial x} (2 x^{2} y) = 4 y x

= 0 - 3 + 0 - 4 y x

簡素化

= - 4 x y - 3