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

解

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

2 x y

解答ステップ

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

x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= x (- 0 + 2 y)

簡素化

= 2 x y