derivative of sqrt(x)-1/(sqrt(x))

解

\frac{d}{d x} (x - \frac{1}{x})

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

解答ステップ

\frac{d}{d x} (x - \frac{1}{x})

和/差の法則を適用:

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

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

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

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

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

簡素化

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