Originally Posted by
skeeter taking the derivative of functions with $\displaystyle \sqrt{x}$ in them are much easier if you remember that its derivative is $\displaystyle \dfrac{1}{2\sqrt{x}}$.
quotient rule ...
$\displaystyle y' = \dfrac{(2\sqrt{x}+3) \cdot \dfrac{1}{2\sqrt{x}} - \sqrt{x} \cdot \dfrac{1}{\sqrt{x}}}{(2\sqrt{x}+3)^2}$
multiply stuff in the numerator and combine like terms ...
$\displaystyle y' = \dfrac{\dfrac{3}{2\sqrt{x}}}{(2\sqrt{x}+3)^2}$
clean it up ...
$\displaystyle y' = \dfrac{3}{2\sqrt{x}(2\sqrt{x}+3)^2}$