#### Answer

$w'(z) = 1 + \frac{1}{2}z^{-\frac{1}{2}}$
So,
$w'(4) = \frac{5}{4}$

#### Work Step by Step

$w(z) = z+\sqrt z$
Therefore,
$w'(z) = 1 + \frac{1}{2}z^{\frac{1}{2} - 1}$
$w'(z) = 1 + \frac{1}{2}z^{-\frac{1}{2}}$
So,
$w'(4) = 1+\frac{1}{4}$
$w'(4) = \frac{5}{4}$