derivative 1/(2sqrt(r))+1/(4r^{3/4)}

解

導関数

\frac{1}{2 r} + \frac{1}{4 r ^{\frac{3}{4}}}

- \frac{1}{4 r ^{\frac{3}{2}}} - \frac{3}{16 r ^{\frac{7}{4}}}

解答ステップ

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

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}{4 r ^{\frac{3}{4}}})

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

\frac{d}{d r} (\frac{1}{4 r ^{\frac{3}{4}}}) = - \frac{3}{16 r ^{\frac{7}{4}}}

= - \frac{1}{4 r ^{\frac{3}{2}}} - \frac{3}{16 r ^{\frac{7}{4}}}