What is this? Absolute value derivative? Magnitude?

[authgeek]

I'm looking at this problem below:

http://apthtml.com/images/deriv.png

The first part I understand - a derivative of some vectors, not a big deal - but the second part is where I'm confused. I can't even come up with a name for it. First I thought magnitude, but I don't really see how that works. My calculus is a little rusty, so bear with me while I ask this question. What is it? How did we get from equation #2 to #3?

Thanks

 

[gabbagabbahey]

It's the magnitude of the vector in #2.

$$\left|\frac{d\textbf{r}}{d\theta}\right|=\left(\frac{d\textbf{r}}{d\theta}\cdot\frac{d\textbf{r}}{d\theta}\right)^{1/2}$$

 

[authgeek]

Thanks! I suppose what threw me off magnitude was the trig functions; they're looking funny when you first do them but they magically boil down to something more manageable.