How do I solve this?
Your answer is not right. You can approach this in either of two ways:
1. Divide the denominator into the numerator to get $\displaystyle f(x) = 3 x^{3/2} + 6x^{1/2} + 5x^{-1/2} $ Now get the derivative using the same techniques as in your other posts, where the derivative of $\displaystyle x^n$ is $\displaystyle n x^{n-1}$.
2. Use the formula for derivates of one function divided by another: the derivative of $\displaystyle \frac {f(x)}{g(x)}$ is: $\displaystyle \frac {f'(x) g(x) - f(x)g'(x)}{(g(x))^2}$. Here $\displaystyle f(x) = 3x^2+6x+5$ and $\displaystyle g(x) = x^{1/2}$.
Both approaches give the same answer.