I've been given this problem and I've been working on it for a week on and off trying to figure out how to simplify it so it looks a bit cleaner. I can get the derivative without issue (I hope it's right) but my simplifying bag-of-tricks is not as developed as it should be.

Original question-- Use logarithmic differentiation to find the derivative:

$\displaystyle y=\frac{3^{-5x}(2x-3)^\frac{4}{3}}{(7x-5)^\frac{2}{5}(3x-7)^\frac{3}{4}}$

$\displaystyle y'=\frac{3^{-5x}(2x-3)^\frac{4}{3}}{(7x-5)^\frac{2}{5}(3x-7)^\frac{3}{4}}[-5ln(3)+\frac{8}{3(2x-3)}-\frac{14}{5(7x-5)}-\frac{9}{4(3x-7)}}]$

Is my instructor just trying to make me go mad or am I missing something? Trying to learn when to stop simplifying is difficult at times.