derivative f(x)=x^{-1/2}+x^{1/2}

解

導関数

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

- \frac{1}{2 x ^{\frac{3}{2}}} + \frac{1}{2 x ^{\frac{1}{2}}}

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (x^{- \frac{1}{2}}) = - \frac{1}{2 x ^{\frac{3}{2}}}

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

= - \frac{1}{2 x ^{\frac{3}{2}}} + \frac{1}{2 x ^{\frac{1}{2}}}