Answer
$G'(r)=\dfrac{1}{2}r^{-1/2}+\dfrac{1}{3}r^{-2/3}$
$G''(r)=-\dfrac{1}{4}x^{-3/2}-\dfrac{2}{9}r^{-5/3}$
Work Step by Step
Rewrite the function
$G(r)=\sqrt{r}+\sqrt[3] r=r^{1/2}+r^{1/3}$
Apply power rule to the function to find the first derivate
$G'(r)=(\dfrac{1}{2})r^{1/2-1}+(\dfrac{1}{3})r^{1/3-1}$
$G'(r)=\dfrac{1}{2}r^{-1/2}+\dfrac{1}{3}r^{-2/3}$
Apply power rule the first derivate to find the second derivate
$G''(r)=\dfrac{1}{2}(-\dfrac{1}{2})r^{-1/2-1}+\dfrac{1}{3}(-\dfrac{2}{3})r^{-2/3-1}$
$G''(r)=-\dfrac{1}{4}x^{-3/2}-\dfrac{2}{9}r^{-5/3}$
