ParametricPlot[{Cos[t]^3, Sin[t]^3}, {t, 0, 2 π}, 
      ImageSize -> 550]

D[a Cos[t]^3, t]

D[a Sin[t]^3, t]

Integrate[3 a Cos[t] Sin[t], {t, 0, π/2}]

4*((3 a)/2)