Answer Happy

Calculate d dt[→r(t)⋅→r'(t)]d dt[r→(t)⋅r→′(t)] and d dt[→u(t)×→r(t)]d dt[u→(t)×r→(t)] forthe vector-valued functions:
Calculate ● d dt -[r(t). F'(t)] and F(t) = cost î+ sint ĵ – e²t k (t) = t Î + sint Ĵ + cost, - [F(t) '(t)] = 8e4t dt d -[ū(t) × r(t)] for the vector-valued functions: dt [u(t) × (t)] = e²t((cos(t) + 2 sin(t)) + cos (2t)) dt (e2t (2t+1) - sin sin(2t)) X Î + Ĵ+ (t cos (t) + sin(t) – cos(2t)) (