D[Cos[t]^2+5Exp[t^3], t]

D[Cos[t]^2+5Exp[t^3], {t, 2}]

tangente[gamma_][t_] :=Simplify[D[gamma[tt], tt]/(D[gamma[tt], tt].D[gamma[tt], tt])^(1/2)] /. tt->t

trifoglioprb[t_] := {Cos[3t]Cos[t], Cos[3t]Sin[t], Cos[3t]^2}

binormale[gamma_][t_] :=Simplify[Cross[D[gamma[tt], tt], D[gamma[tt], {tt,2}]]/(Cross[D[gamma[tt], tt], D[gamma[tt], {tt,2}]].Cross[D[gamma[tt], tt], D[gamma[tt], {tt,2}]])^(1/2)]/. tt -> t

normale[gamma_][t_] := Simplify[Cross[binormale[gamma][tt], tangente[gamma][tt]]] /. tt -> t

Show[{ParametricPlot3D[trifoglioprb[t], {t,0, 2Pi}], Graphics3D[{PointSize[0.03], Red, Point[trifoglioprb[Pi/5]]}], Graphics3D[{Thick, Green, Arrow[{trifoglioprb[Pi/5],trifoglioprb[Pi/5]+tangente[trifoglioprb][Pi/5]/5}]}]}]

Show[ParametricPlot3D[trifoglioprb[t], {t,0, 2Pi}], Graphics3D[{PointSize[0.02], Red, Point[trifoglioprb[Pi/5]]}], Graphics3D[{Thick, Green, Arrow[{trifoglioprb[Pi/5],trifoglioprb[Pi/5]+tangente[trifoglioprb][Pi/5]/3}]}],Graphics3D[{Thick, Blue, Arrow[{trifoglioprb[Pi/5],trifoglioprb[Pi/5]+normale[trifoglioprb][Pi/5]/3}]}],Graphics3D[{Thick, Orange, Arrow[{trifoglioprb[Pi/5],trifoglioprb[Pi/5]+binormale[trifoglioprb][Pi/5]/3}]}]]

Manipulate[Show[ParametricPlot3D[trifoglioprb[t], {t,0, 2Pi}], Graphics3D[{PointSize[0.02], Red, Point[trifoglioprb[k]]}], Graphics3D[{Thick, Green, Arrow[{trifoglioprb[k],trifoglioprb[k]+tangente[trifoglioprb][k]/3}]}],Graphics3D[{Thick, Blue, Arrow[{trifoglioprb[k],trifoglioprb[k]+normale[trifoglioprb][k]/3}]}],Graphics3D[{Thick, Orange, Arrow[{trifoglioprb[k],trifoglioprb[k]+binormale[trifoglioprb][k]/3}]}]], {k, 0.1, 2Pi}]