(\partial)/(\partial y)(-3x^2+7xy-4y^2+x+y)

解

\frac{\partial}{\partial y} (- 3 x^{2} + 7 x y - 4 y^{2} + x + y)

7 x + 1 - 8 y

解答ステップ

\frac{\partial}{\partial y} (- 3 x^{2} + 7 x y - 4 y^{2} + x + y)

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} (3 x^{2}) + \frac{\partial}{\partial y} (7 x y) - \frac{\partial}{\partial y} (4 y^{2}) + \frac{\partial}{\partial y} (x) + \frac{\partial}{\partial y} (y)

\frac{\partial}{\partial y} (3 x^{2}) = 0

\frac{\partial}{\partial y} (7 x y) = 7 x

\frac{\partial}{\partial y} (4 y^{2}) = 8 y

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

\frac{\partial}{\partial y} (y) = 1

= - 0 + 7 x - 8 y + 0 + 1

簡素化

= 7 x + 1 - 8 y