(\partial)/(\partial x)(3x^2-2x+6y^2+2y+2)

解

\frac{\partial}{\partial x} (3 x^{2} - 2 x + 6 y^{2} + 2 y + 2)

6 x - 2

解答ステップ

\frac{\partial}{\partial x} (3 x^{2} - 2 x + 6 y^{2} + 2 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) + \frac{\partial}{\partial x} (6 y^{2}) + \frac{\partial}{\partial x} (2 y) + \frac{\partial}{\partial x} (2)

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

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

\frac{\partial}{\partial x} (6 y^{2}) = 0

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

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

= 6 x - 2 + 0 + 0 + 0

簡素化

= 6 x - 2