We have that for all . Thus is identically 0 in . Just apply the chain rule.
I was thinking about using the chain rule because
(Dh)_t = ((Dh)_a(t)) o (Da)_t where I believe ((Dh)_a(t))=(grad h)(a(t))
but couldn't really relate this to a dot product that would be 0.
Any help would be greatly appreciated. Thanks