(\partial)/(\partial x)(5x+10y+10xy)

解

\frac{\partial}{\partial x} (5 x + 10 y + 10 x y)

10 y + 5

解答ステップ

\frac{\partial}{\partial x} (5 x + 10 y + 10 x 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 x) + \frac{\partial}{\partial x} (10 y) + \frac{\partial}{\partial x} (10 x y)

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

\frac{\partial}{\partial x} (10 y) = 0

\frac{\partial}{\partial x} (10 x y) = 10 y

= 5 + 0 + 10 y

簡素化

= 10 y + 5