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

解

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

8 x

解答ステップ

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

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

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

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

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

= 8 x - 0 + 0

簡素化

= 8 x