Scalar Product of a diffrential.

[raisin_raisin]

Hey, in my textbook they keep doing this and I can't follow
for example r.$$\ddot{}r$$ = 1/2 $$\ddot{}r^{}^2{}$$
and r.$$\dot{}r$$ = 1/2 $$\dot{}r^2{}$$.

Can anyone explain this to me? I know I should probably know it.

P.S Can't quite get the dot product to look right apologies.

 

[AKG]

(r²)' = 2rr' by chain rule. Or if the r's are supposed to be vector functions:

(r.r)'
= r'.r + r.r' by product rule for dot product
= r.r' + r.r' by commutativity of dot product
= 2r.r'