Proving Vector Properties

is X cross product?
[R(t) X R'(t)]' = R'(t) X R'(t)+R(t) X R"(t)
for any sensible derivative
thus
[R(t) X R'(t)]' = R(t) X R"(t)
if and only if
R'(t) X R'(t)=0
clearly true for cross product

 

Is the "Dt" derivative with respect to t? i.e.(R x R')' ?

What have you tried? Have you tried actually writing out each side in terms of derivatives of f, g, and h?

Do you know that the "product rule" from Calculus I is still true for vector products? What does that give you?