Step by step for related rates with chain rule?

I have the following function in terms of time:

$\displaystyle M(t) = \sqrt{x(t)^2 + y(t)^2}$

I know the differentiation with respect to t is:

$\displaystyle M'(t) = \frac{xx' + yy'}{\sqrt{x^2 + y^2}}$

However, I don't know how to do the differentiation to get that answer. I know the chain rule needs to be used, but I don't know exactly how to use it. Could someone please help me understand? My textbook is not as clear as I had hoped, and it unfortunately skips steps.