let f(x) = (sqrt(x) - 3)/(sqrt(x) + 3). then, f(x) = (3x^(3/2))/((x^2 + 3)^2) f(5) =

Explanation:

Step1: Substitute x = 5 into f'(x)

Given (f'(x)=\frac{3x^{\frac{3}{2}}}{(x + 3)^2}), substitute (x = 5).

Step2: Calculate the numerator

The numerator is (3\times5^{\frac{3}{2}}=3\times5\times\sqrt{5}=15\sqrt{5}).

Step3: Calculate the denominator

The denominator is ((5 + 3)^2=64).

Answer:

(\frac{15\sqrt{5}}{64})