import math

# Define the function f$($x$)$

def f$($x$)$:

return math.sqrt$($x$)*$ math.log$($x$)$

# Define the exact derivative function f$\text{'}($x$)$

def fp$($x$)$:

return $(0\mathrm{.}5*$ math.log$($x$))+($math$.$sqrt$($x$)/$ x$)$

# Define the approximation function for the derivative f$\text{'}($x$)$

def fp$\_$approx$($f$,$ a$,$ h$)$:

return $($f$($a $+$ h$)-$ f$($a$))/$ h

# Calculate the absolute difference between exact value and approximation

def absolute$\_$difference$($f$,$ a$,$ h$)$:

exact$\_$value $=$ fp$($a$)$

approx$\_$value $=$ fp$\_$approx$($f$,$ a$,$ h$)$

return abs$($exact$\_$value $-$ approx$\_$value$)$

# Calculate the magnitude of the difference when a $=6$ and h $=0\mathrm{.}8$

a $=6$

h $=0\mathrm{.}8$

difference $=$ absolute$\_$difference$($f$,$ a$,$ h$)$

print$($round$($difference$,4))$