code: def _dphiTilde(self, r, N, L):
          
          a = self._a
          l = nu.arange(0, L, dtype=float)[nu.newaxis, :]
          n = nu.arange(0, N, dtype=float)[:, nu.newaxis]
          xi = self._calculateXi(r)
          dC = _dC(xi,N,L)
          return -(4*nu.pi)**.5 * (nu.power(a*r, l)*(l*(a + r)*nu.power(r,-1) -(2*l + 1))/((a + r)**(2*l + 2))*_C(xi,N,L) + 
          a**-1*(1 - xi)**2 * (a*r)**l / (a + r)**(2*l + 1) *dC/2.)
docs: NAME:
             _dphiTilde
          PURPOSE:
             Evaluate the derivative of phiTilde with respect to r
          INPUT:
             r - spherical radius
             N - size of the N dimension
             L - size of the L dimension
          OUTPUT:
             the derivative of phiTilde with respect to r
          HISTORY:
             2016-06-06 - Written - Aladdin