Answer
$\dfrac{5}{4}$
Work Step by Step
Use derivative formula; $f(x)= x^n \implies f'(x)= n x^{n-1}$
Consider $w(z) = z+\sqrt z$
Now, $w'(z) = 1 + (\dfrac{1}{2})z^{(1/2) - 1}=1 + \dfrac{1}{2}z^{-(1/2)}$
Then, we have $w'(4) =1 + \dfrac{1}{2}(4)^{-(1/2)}= 1+\dfrac{1}{4}= \dfrac{5}{4}$
