What is the derivative of g(w)= 8/(3w^5)+9sqrt(w) ?

The derivative of g(w)= 8/(3w^5)+9sqrt(w) is (-80+27w^{11/2})/(6w^{11/2)sqrt(w)}

What is the first derivative of g(w)= 8/(3w^5)+9sqrt(w) ?

The first derivative of g(w)= 8/(3w^5)+9sqrt(w) is (-80+27w^{11/2})/(6w^{11/2)sqrt(w)}

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(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}

Simplify

- \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}

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What is the derivative of g(w)= 8/(3w^5)+9sqrt(w) ?
The derivative of g(w)= 8/(3w^5)+9sqrt(w) is (-80+27w^{11/2})/(6w^{11/2)sqrt(w)}
What is the first derivative of g(w)= 8/(3w^5)+9sqrt(w) ?
The first derivative of g(w)= 8/(3w^5)+9sqrt(w) is (-80+27w^{11/2})/(6w^{11/2)sqrt(w)}