find the derivative
g(x)= ln x^(3/4)/((3x+5)^5)
what an ugly function ...
$\displaystyle g(x) = \frac{3}{4} \cdot \frac{\ln{x}}{(3x+5)^5}$
$\displaystyle g'(x) = \frac{3}{4} \cdot \frac{(3x+5)^5 \cdot \frac{1}{x} - \ln{x} \cdot 15(3x+5)^4}{(3x+5)^{10}}$
$\displaystyle g'(x) = \frac{3}{4} \cdot \frac{(3x+5) \cdot \frac{1}{x} - \ln{x} \cdot 15}{(3x+5)^6}$
$\displaystyle g'(x) = \frac{3(3x+5) - 15x\ln{x}}{4x(3x+5)^6}$
then you should have used brackets to indicate ln[your expression], like so ...
g(x)= ln[x^(3/4)/((3x+5)^5)]
or ...
$\displaystyle g(x) = \ln\left[\frac{x^{\frac{3}{4}}}{(3x+5)^5}\right]$
use the laws of logs to break up the expression into several logs, then find the derivative of each logarithmic term.
$\displaystyle
\ln\left[\frac{x^{\frac{3}{4}}}{(3x+5)^5}\right] = \frac{3}{4}\ln{x} - 5\ln(3x+5)$