(\partial)/(\partial x)(9-x^2+xy-4y^2)

解

\frac{\partial}{\partial x} (9 - x^{2} + x y - 4 y^{2})

y - 2 x

解答ステップ

\frac{\partial}{\partial x} (9 - x^{2} + x y - 4 y^{2})

y

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 x} (9) - \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (x y) - \frac{\partial}{\partial x} (4 y^{2})

\frac{\partial}{\partial x} (9) = 0

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

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

\frac{\partial}{\partial x} (4 y^{2}) = 0

= 0 - 2 x + y - 0

簡素化

= y - 2 x