derivative y=1+x-4x^{1/2}

解

導関数

y = 1 + x - 4 x^{\frac{1}{2}}

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

解答ステップ

\frac{d}{d x} (1 + x - 4 x^{\frac{1}{2}})

和/差の法則を適用:

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

= \frac{d}{d x} (1) + \frac{d x}{d x} - \frac{d}{d x} (4 x^{\frac{1}{2}})

\frac{d}{d x} (1) = 0

\frac{d x}{d x} = 1

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

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

簡素化

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