I'm having a little trouble with part of this problem, specifically, finding the derivative of $\sqrt{625-x^2}$. Wolfram Alpha tells me to "use the chain rule $\frac{d}{dx}(\sqrt{625-x^2})=\frac{d\sqrt{u}}{du}\frac{du}{dx}$, where $u=625-x^2$ and $\frac{d\sqrt{u}}{du}=\frac{1}{2\sqrt{u}}$. " Which I don't really get. Is there a different way to do this, or am I maybe just missing something obvious?

EDIT: Oh also, I understand that the derivative would be $\frac{x}{\sqrt{625-x^2}}$, but only because it was done out the "long" way in section 2.1 of the book. I'm basically trying to understand how it's done with the shortcuts we've been using.

EDIT AGAIN: Wow, so I just noticed at the end of the notes that we got on Monday, Dana mentions exactly this. Oops.