derivative 1/(2sqrt(x))+1/(6x^{5/6)}

解

導関数

\frac{1}{2 x} + \frac{1}{6 x ^{\frac{5}{6}}}

- \frac{1}{4 x ^{\frac{3}{2}}} - \frac{5}{36 x ^{\frac{11}{6}}}

解答ステップ

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{6 x ^{\frac{5}{6}}})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{1}{2 x}) + \frac{d}{d x} (\frac{1}{6 x ^{\frac{5}{6}}})

\frac{d}{d x} (\frac{1}{2 x}) = - \frac{1}{4 x ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{1}{6 x ^{\frac{5}{6}}}) = - \frac{5}{36 x ^{\frac{11}{6}}}

= - \frac{1}{4 x ^{\frac{3}{2}}} - \frac{5}{36 x ^{\frac{11}{6}}}