proposition: Lemma D_Rsqr_u_epsilon_1 : forall (eps : posreal) (t : R), derive_pt (fun y : R => Rsqr (u eps y)) t (fct_der2 eps t) = (2 * u eps t * derive_pt (u eps) t (d_u eps t))%R.
proof: Proof. intros; set (f := u eps). cut (derivable_pt f t); [ intro H | apply (d_u eps t) ]. cut (derive_pt f t H = derive_pt f t (d_u eps t)); [ intro | apply pr_nu ]. reg. Qed.
imports: Reals trajectory_const rrho trajectory_def constants