<s>[INST] Differentiate and simplify. $m(x) = \frac{x}{\sqrt{4x-3}}$ My work so far is:
\begin{align}
m'(x) &= \frac{(1)(\sqrt{4x-3})-(x)(1/2)(4x-3)^{-1/2}(4)}{(\sqrt{4x-3})^2} \\
&= \frac{\sqrt{4x-3} - 2x(4x-3)^{1/2}}{4x-3}
\end{align}
and now I'm stuck on how to simplify further
 [/INST] One method for differentiating $m(x)$ is treating $m(x)=\frac{f(x)}{g(x)}$ with 
$f(x)=x$ and $g(x)=\sqrt{4x-3}$  and using the quotient rule for differentiation.
Then $m'(x)=\frac{g(x)f'(x)-f(x)g'(x)}{g(x)^2}=\frac{\sqrt{4x-3}-(x\frac{2}{\sqrt{4x-3}})}{4x-3}$.
Simplyfying we obtain the desired result $m'(x)=\frac{2x-3}{\sqrt{(4x-3)^{3}}}$.
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