This is an easy question. Doing logarithmic differentiation, heres the problem:
How do they get from y'=y(7/2 + 7/2 ln x) to the next step? I got everything else.
Well first of, they moved $\displaystyle \frac{7}{2}$ out of the brackets, like so:
$\displaystyle y'=y\frac{7}{2}(1+ln(x))$
And then replaced $\displaystyle y$, with $\displaystyle (\sqrt{x})^{7x}$, because they said that $\displaystyle y=(\sqrt{x})^{7x}$ in the beginning.