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

解

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

6 x - 2 y

解答ステップ

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

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

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

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

= 6 x - 2 y + 0

簡素化

= 6 x - 2 y