(\partial)/(\partial y)(x^2-4xy+3y^2)

解

\frac{\partial}{\partial y} (x^{2} - 4 x y + 3 y^{2})

6 y - 4 x

解答ステップ

\frac{\partial}{\partial y} (x^{2} - 4 x y + 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^{2}) - \frac{\partial}{\partial y} (4 x y) + \frac{\partial}{\partial y} (3 y^{2})

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

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

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

= 0 - 4 x + 6 y

簡素化

= 6 y - 4 x