To differentiate the given function, we can start by finding the derivative of each term using the chain rule.

Let f(x) = √(3x - 6) and g(x) = √(2x - 11).

Then, the derivative of f(x) with respect to x can be found by using the power rule for differentiation:

f'(x) = (1/2)(3x - 6)^(-1/2) * 3
f'(x) = 3 / (2√(3x - 6))

Similarly, the derivative of g(x) with respect to x is:

g'(x) = (1/2)(2x - 11)^(-1/2) * 2
g'(x) = 2 / (2√(2x - 11))
g'(x) = 1 / √(2x - 11)

Now, to find the derivative of U = √(3x - 6) + √(2x - 11), we can use the chain rule:

U' = f'(x) + g'(x)
U' = 3 / (2√(3x - 6)) + 1 / √(2x - 11)

Therefore, the derivative of the function U = √(3x - 6) + √(2x - 11) is U' = 3 / (2√(3x - 6)) + 1 / √(2x - 11).