derivative of cubic spline for use in nonlinear optimization

Hi

i wanna solve a functional system of nonlinear equations by collocation. To speed up the solution process i want to provide derivatives to the solver. The system includes cubic splines. So far I use Matlab's csapi to produce the cubic spline. To provide derivatives of the system, i need the derivatives of the output of csapi wrt the values of the function I interpolate at the grid points. (Either derivatives of the polynomical coefficients or even better of the evaluated polynomial). Does anyone have code for this?

Formally:

Be:

Spline=csapi(grid,functionvalues)

Interpolatedvalue=fnval(Spline,querypoint)

Then I need:

d Spline.coefs / d functionvalues

Or better:

d Interpolatedvalue / d functionvalues

Many thanks!