Instantaneous frequency calculation with Stockwell Transform code

I calculate a signal with stockwell transform and want to get the instantaneous frequency of it.

so I write a code to calculate the Derivative of ST .

BUT it seems wrong,I change the gauss window of the stran fuction.

W=2*pi*repmat(f,nhaf,1).*repmat(invfk,1,N);

dW=2*pi*repmat(invfk,1,N);

G=exp((-W.^2)/2);

G=(-W.*dW).*G;

why it is wrong?AND how can I rewrite?