find the derivative formula

r  =     x                  ln(x)             ln(2)

        ____     -       ____     +

        3³√x                9

Note  that we can write this as :

r  = (1/3)x^(2/3) -  (1/9)ln(x)  +  ln (2)      so.....

We can use the Power Rule on the first term

And the definition of the derivative of ln(x)  on the second term

Note....the third term is a constant...its derivative is  0

So we have.....

dr

__    =   (2/9)x^(-1/3) - (1/9)(1/x)  =  

dx

   2                   1

 ____     -       ___        =

 9³√x               9x

[ 2 ³√x^2  -  1    ]

_____________

          9x