Finding the derivative of an integral $$g(x) = \int_{2x}^{6x} \frac{u+2}{u-4}du $$
For finding the $ g'(x)$, would I require to find first the derivative of $\frac{u+2}{u-4}$ 
then Replace the $u$ with 6x and 2x and add them ?
(the 2x would have to flip so the whole term is negative)
If the previous statement is true would the final showdown be the following:
$$ \frac{6}{(2x-4)^2} - \frac{6}{(6x-4)^2}$$  

According to Leibniz integral rule 
$$g'(x)=f(6x)\times 6-f(2x)\times 2$$ wherein $f(t)=\large \frac{t+2}{t-4}$.
