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

解

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

2 x y - 6 y

解答ステップ

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

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

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

\frac{\partial}{\partial y} (6 x^{2}) = 0

\frac{\partial}{\partial y} (3 y^{2}) = 6 y

= 2 x y - 0 - 6 y

簡素化

= 2 x y - 6 y