40. Correct. The answer is true. Using the product rule: d/dt(t³lnt²)= 3t²lnt² + 2t⁴/t² = 3t²lnt² + 2t²= 3t²*2lnt + 2t². Factor out 2t² to get (3lnt + 1)2t²_. In general, d/dt[lnf(t)] = f'(t)/f(t) and ln(t^a) = alnt.