derivative g(w)= 8/(3w^5)+9sqrt(w)

解答

导数

g (w) = \frac{8}{3 w ^{5}} + 9 w

\frac{- 80 + 27 w ^{\frac{11}{2}}}{6 w ^{\frac{11}{2}} w}

求解步骤

\frac{d}{d w} (\frac{8}{3 w ^{5}} + 9 w)

使用微分加减法定则:

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

= \frac{d}{d w} (\frac{8}{3 w ^{5}}) + \frac{d}{d w} (9 w)

\frac{d}{d w} (\frac{8}{3 w ^{5}}) = - \frac{40}{3 w ^{6}}

\frac{d}{d w} (9 w) = \frac{9}{2 w}

= - \frac{40}{3 w ^{6}} + \frac{9}{2 w}

化简

- \frac{40}{3 w ^{6}} + \frac{9}{2 w} : \frac{- 80 + 27 w ^{\frac{11}{2}}}{6 w ^{\frac{11}{2}} w}

= \frac{- 80 + 27 w ^{\frac{11}{2}}}{6 w ^{\frac{11}{2}} w}