(\partial)/(\partial y)((x^2-1)(y+2))

解

\frac{\partial}{\partial y} ((x^{2} - 1) (y + 2))

x^{2} - 1

解答ステップ

\frac{\partial}{\partial y} ((x^{2} - 1) (y + 2))

x

を定数として扱う

定数を除去:

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

= (x^{2} - 1) \frac{\partial}{\partial y} (y + 2)

和/差の法則を適用:

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

= (x^{2} - 1) (\frac{\partial}{\partial y} (y) + \frac{\partial}{\partial y} (2))

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

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

= (x^{2} - 1) (1 + 0)

簡素化

= x^{2} - 1