(\partial)/(\partial x)((y)(x^2+xy-10))

解

\frac{\partial}{\partial x} ((y) (x^{2} + x y - 10))

y (y + 2 x)

解答ステップ

\frac{\partial}{\partial x} ((y) (x^{2} + x y - 10))

y

を定数として扱う

定数を除去:

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

= y \frac{\partial}{\partial x} (x^{2} + x y - 10)

和/差の法則を適用:

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

= y (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (x y) - \frac{\partial}{\partial x} (10))

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

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

\frac{\partial}{\partial x} (10) = 0

= y (2 x + y - 0)

簡素化

= y (y + 2 x)