derivative 1/(2sqrt(r))+1/(9r^{8/9)}

解

導関数

\frac{1}{2 r} + \frac{1}{9 r ^{\frac{8}{9}}}

- \frac{1}{4 r ^{\frac{3}{2}}} - \frac{8}{81 r ^{\frac{17}{9}}}

解答ステップ

\frac{d}{d r} (\frac{1}{2 r} + \frac{1}{9 r ^{\frac{8}{9}}})

和/差の法則を適用:

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

= \frac{d}{d r} (\frac{1}{2 r}) + \frac{d}{d r} (\frac{1}{9 r ^{\frac{8}{9}}})

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

\frac{d}{d r} (\frac{1}{9 r ^{\frac{8}{9}}}) = - \frac{8}{81 r ^{\frac{17}{9}}}

= - \frac{1}{4 r ^{\frac{3}{2}}} - \frac{8}{81 r ^{\frac{17}{9}}}