#### Answer

$f’(x) = 1$

#### Work Step by Step

$f(x) = (x^{\frac{1}{2}}+1)(x^{\frac{1}{2}}-1); $ $ x\geq 0 $
Product and Power Rules:
$f’(x) = \frac{1}{2}( x^{-\frac{1}{2}})(x^{\frac{1}{2}}-1) + \frac{1}{2}( x^{-\frac{1}{2}})(x^{\frac{1}{2}}+1) $
$f’(x) = \frac{1}{2} (1-x^{-\frac{1}{2}}) + \frac{1}{2}(1+ x^{-\frac{1}{2}}) $
$f’(x) = \frac{1}{2} (1-x^{-\frac{1}{2}} + 1+ x^{-\frac{1}{2}}) $
$f’(x) = \frac{1}{2} (2) $
$f’(x) = 1 $