Answer
$$\frac{1}{10}\sqrt[10]{\frac{3 x+4}{2 x-4}} \left( \frac{3}{ 3 x+4}-\frac{ 2}{2 x-4}\right)$$
Work Step by Step
Given
$$
y=\sqrt[10]{\frac{3 x+4}{2 x-4}}
$$
Since
\begin{align*}
\ln y&= \frac{1}{10} \ln \frac{3 x+4}{2 x-4}\\
&= \frac{1}{10}\left( \ln (3 x+4)-\ln (2 x-4)\right)\\
\end{align*}
Differentiate both sides; we get
\begin{align*}
\frac{y'}{y}&= \frac{1}{10}\left( \frac{3}{ 3 x+4}-\frac{ 2}{2 x-4}\right)\\
y'&= \frac{y}{10}\left( \frac{3}{ 3 x+4}-\frac{ 2}{2 x-4}\right)\\
&=\frac{1}{10}\sqrt[10]{\frac{3 x+4}{2 x-4}} \left( \frac{3}{ 3 x+4}-\frac{ 2}{2 x-4}\right)
\end{align*}
