#### Answer

$u'= \frac{5x-1}{4x\sqrt{x}}$
$u'= \frac{5x-1}{4x^{3/2}}$

#### Work Step by Step

$u = \frac{5x+1}{2\sqrt x}$
quotient rule:
$u' = \frac{2\sqrt x(5) - (5x+1)x^{-\frac{1}{2}}}{4x}$
$u' = \frac{10\sqrt x - 5\sqrt x-x^{-\frac{1}{2}})}{4x}$
$u' = \frac{5\sqrt x-x^{-\frac{1}{2}}}{4x}$
$u'= \frac{5x-1}{4x\sqrt{x}}$
$u'= \frac{5x-1}{4x^{3/2}}$