Letbe a v.v.f -with the first and second derivativesr(t)andr'. Determine formula forr''

-in terms ofd/dt [r.(r' x r'')]:r

How do we approach this one?

maybe:

??d/dt [r.(r' x r'')] = d/dt [r.r' x r.r''] = ((r'.r' + r.r'') x r'.r'') + (r.r' x (r'.r'' + r.r'''))

...and then what? I probably looking at this completely wrong -- there must be some simple vector calculus identities that make this easy or something.

Is anyone able to give me a starting point -- or starting direction? -- thanks heaps