f ′ ( t ) = − 2000 t 2 − 10000 ( t 2 + 5 ) 2 với t ≥ 0 .

b) Sai.

\[f'\left( t \right) = {\left( {400} \right)^\prime } + \frac{{{{\left( {2000t} \right)}^\prime }\left( {{t^2} + 5} \right) - {{\left( {{t^2} + 5} \right)}^\prime }2000t}}{{{{\left( {{t^2} + 5} \right)}^2}}} = \frac{{2000\left( {{t^2} + 5} \right) - 2t.2000t}}{{{{\left( {{t^2} + 5} \right)}^2}}}\]\[ = \frac{{ - 2000{t^2} + 10000}}{{{{\left( {{t^2} + 5} \right)}^2}}}\].