Find the derivative of the function.
\[
y=\sqrt{\frac{x}{x+5}}
\]
\[
y^{\prime}=
\]

Step 1 ：Given the function \(y = \sqrt{\frac{x}{x + 5}}\)

Step 2 ：We need to find the derivative of this function. To do this, we will use the chain rule, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 3 ：In this case, the outer function is the square root function and the inner function is the fraction \(\frac{x}{x+5}\).

Step 4 ：We will also need to use the quotient rule when differentiating the inner function. The quotient rule states that the derivative of a quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the square of the denominator.

Step 5 ：Applying these rules, we find that the derivative of the function is given by the expression \(\sqrt{\frac{x}{x + 5}}*(x + 5)*(-x/(2*(x + 5)^2) + 1/(2*(x + 5)))/x\)

Step 6 ：This expression can be simplified further to \(\frac{5\sqrt{\frac{x}{x + 5}}}{2x(x + 5)}\)

Step 7 ：Final Answer: The derivative of the function \(y = \sqrt{\frac{x}{x + 5}}\) is given by \(\boxed{\frac{5\sqrt{\frac{x}{x + 5}}}{2x(x + 5)}}\)