dbspline(u,k);

%calculates the derivative of kth basis function of a cubic B-spline
function value = dbspline(u,k);

sz =size(u);
value = zeros(sz(1),sz(2));
loc = find(k == 0); 
        value(loc) = (-3*(1-u(loc)).^2)./6;
loc = find(k == 1);
        value(loc) = (9*(u(loc).^2)-12*(u(loc)))./6;
loc = find(k == 2);
        value(loc) = (-9*(u(loc).^2)+6*(u(loc))+ 3)./6;
loc = find(k == 3);
        value(loc) = (3*u(loc).^2)./6;