(\partial)/(\partial x)(4x^{0.5}+2x^{0.25})

解

\frac{\partial}{\partial x} (4 x^{0.5} + 2 x^{0.25})

\frac{2 x ^{0.25} + 0.5}{x ^{0.75}}

解答ステップ

\frac{\partial}{\partial x} (4 x^{0.5} + 2 x^{0.25})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (4 x^{0.5}) + \frac{\partial}{\partial x} (2 x^{0.25})

\frac{\partial}{\partial x} (4 x^{0.5}) = \frac{2}{x ^{0.5}}

\frac{\partial}{\partial x} (2 x^{0.25}) = \frac{0.5}{x ^{0.75}}

= \frac{2}{x ^{0.5}} + \frac{0.5}{x ^{0.75}}

簡素化

\frac{2}{x ^{\frac{1}{2}}} + \frac{0.5}{x ^{0.75}} : \frac{2 x ^{0.25} + 0.5}{x ^{0.75}}

= \frac{2 x ^{0.25} + 0.5}{x ^{0.75}}