(\partial)/(\partial x)(2x^2+4y^2+1/2)

解

\frac{\partial}{\partial x} (2 x^{2} + 4 y^{2} + \frac{1}{2})

4 x

解答ステップ

\frac{\partial}{\partial x} (2 x^{2} + 4 y^{2} + \frac{1}{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} (2 x^{2}) + \frac{\partial}{\partial x} (4 y^{2}) + \frac{\partial}{\partial x} (\frac{1}{2})

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

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

\frac{\partial}{\partial x} (\frac{1}{2}) = 0

= 4 x + 0 + 0

簡素化

= 4 x