differentiating a fit formula

I wish to extract the fit formula or function along with its coefficients, then differentiate it to get its derivative function and also integrate the fit function to get its integration. How to do that please suggest.

load dataset.mat
x=dataset(:,1);y=dataset(:,2);
[fit, gof] = createFit(x, y)
fx = differentiate(fit,x);
df_fit=(x.^2)*3+2*x.+1;
plot(x,[fx-dif_fit])

function [fitresult, gof] = createFit(x, y)
% Fit: 'untitled fit 1'.
[xData, yData] = prepareCurveData( x, y );

% Set up fittype and options.
ft = fittype( 'poly3' );

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft );

end

Answer 1

[Walter Roberson]

differentiate is specifically designed to differentiate cfit and sfit objects.

integrate is designed to integrate cfit objects.

[Josh]

Thanks for the answer. As we manually differentiate the fit function and compare it to the values of the fx, they are not the same. How so!! Please suggest.

[Walter Roberson]

df_fit=(x.^2)*3+2*x.+1; is the derivative of x^3 + x^2 + x + const but poly3 is going to create a model of the form a*x^3 + b*x^2 + c*x + const which would have a derivative of 3*a*x^2 + 2*b*x + c

[Torsten]

Isn't the derivative with respect to the fitting parameters required here ? [x.^3,x.^2,x] ?