derivative 4sqrt(x)-3/(x^6)

解

derivative

\frac{2 ( x ^{\frac{13}{2}} + 9 )}{x ^{\frac{13}{2}} x}

解答ステップ

\frac{d}{d x} (4 x - \frac{3}{x ^{6}})

和/差の法則を適用:

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

= \frac{d}{d x} (4 x) - \frac{d}{d x} (\frac{3}{x ^{6}})

\frac{d}{d x} (4 x) = \frac{2}{x}

\frac{d}{d x} (\frac{3}{x ^{6}}) = - \frac{18}{x ^{7}}

= \frac{2}{x} - (- \frac{18}{x ^{7}})

簡素化

\frac{2}{x} - (- \frac{18}{x ^{7}}) : \frac{2 ( x ^{\frac{13}{2}} + 9 )}{x ^{\frac{13}{2}} x}

= \frac{2 ( x ^{\frac{13}{2}} + 9 )}{x ^{\frac{13}{2}} x}