Find the derivative of $y=x\sqrt{9-x}$ "Find the derivative of $y=x\sqrt{9-x}$."
So this is what I have and now I'm stuck.
\begin{align}
y' &= x \frac{d}{dx}\left[(9-x)^{1/2}\right] + (9-x)^{1/2} \frac{d}{dx}(x)\\
   &= x \left[\frac{1}{2}(9-x)^{-1/2}\right] + (9-x)^{1/2} (1)
\end{align}
So I now that I need to multiply and simplify but I don't know where to start. Help!
This problem is actually part of a homework question where I have to analyze a graph and find critical points and min and max.

Just for fun, an alternate approach:
$$\begin{align}
y&= x\sqrt{9-x}\\
y^2&=9x^2-x^3\\
2yy'&=18x-3x^2\\
y'&=\frac{18x-3x^2}{2y}\\
y'&=\frac{18x-3x^2}{2x\sqrt{9-x}}\\
y'&=\frac{18-3x}{2\sqrt{9-x}}
\end{align}$$
