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

解

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

\frac{2}{x ^{\frac{1}{2}}}

解答ステップ

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

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

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

= \frac{2}{x ^{\frac{1}{2}}} + 0

簡素化

= \frac{2}{x ^{\frac{1}{2}}}