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

解

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

2 y - 2 x

解答ステップ

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

x

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

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

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

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

= 2 y - 2 x + 0

簡素化

= 2 y - 2 x