  Two species superfluid Fermi gas is investigated on the BCS side up to the
Feshbach resonance. Using the Greens's function technique gradient corrections
are calculated to the generalized Thomas-Fermi theory including Cooper pairing.
Their relative magnitude is found to be measured by the small parameter
$(d/R_{TF})^4$, where $d$ is the oscillator length of the trap potential and
$R_{TF}$ is the radial extension of the density $n$ in the Thomas-Fermi
approximation. In particular at the Feshbach resonance the universal %constant
$A_{TF}$ has the %correction in the center $A=A_{TF}+A_2(d/R_{TF})^4+\...$
corrections to the local density approximation are calculated and a universal
prefactor $\kappa_W=7/27$ is derived for the von Weizs\"acker type correction
$\kappa_W(\hbar^2/2m)(\nabla^2 n^{1/2}/n^{1/2})$.
