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Can someone explain this please?

In a solution to a problem I am given that:

xdxdt+ydydt=0x\frac{dx}{dt} + y\frac{dy}{dt} =0

And thus:

ddt(12(x2+y2))=0\frac{d}{dt} (\frac{1}{2}(x^2 + y^2)) = 0

Can anyone explain this to me, it seems pretty obvious but I can't explain why the first bit actually gives the second bit.
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DFranklin
18
Work from the 2nd part to the first. (It's harder to go the other way, and you more or less need to spot it).

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