Hi I am a bit confused on how to differentiate a fraction like the problem:
integral of 2 / (3 x^1/3) dx
Im not sure where to start can you pull the 2/3 out front and just make it:
1/ x^1/3? and take ln of x^1/3?
Please help?
the natural log only comes into play if you have 1/x, which you do not have.
note that $\displaystyle \frac 2{3x^{1/3}} = \frac 23x^{-1/3}$. now integrate that using the power rule for integrals $\displaystyle \left( \int x^n~dx = \frac {x^{n + 1}}{n + 1} + C \text{ for } n \ne -1 \right)$