Answer
$ -\displaystyle \frac{4}{3}(4x-1)^{1/2}(x-1) $
Work Step by Step
$\left[ (4x-1)^{3/2} =(4x-1)^{1+1/2}=(4x-1)(4x-1)^{1/2} \right]$
$(4x-1)^{1/2}-\displaystyle \frac{1}{3}(4x-1)^{3/2}=(4x-1)^{1/2}-\frac{1}{3}(4x-1)(4x-1)^{1/2}$
... factor out $(4x-1)^{1/2}$
$=(4x-1)^{1/2}[1-\displaystyle \frac{1}{3}(4x-1)]$
$=(4x-1)^{1/2}[1-\displaystyle \frac{4}{3}x+\frac{1}{3}]$
$=(4x-1)^{1/2}(\displaystyle \frac{4}{3}-\frac{4}{3}x)$... factor out $-\displaystyle \frac{4}{3}$
$=-\displaystyle \frac{4}{3}(4x-1)^{1/2}(x-1) $
