Sensitivity analysis using finite differences

Please I need help obtaining the sensitivity of the outputs of a system with respect to the inputs using finite difference. I tried to follow this question https://www.mathworks.com/matlabcentral/answers/328722-matlab-simple-loop-for-different-function-variables-finite-difference but I can seem to figure it out.

So in my case the right hand side of my differential equation :

dy/dt= f(x,u)

dy/dt=[u1 - x9;

u2 - x10;

x9+ x11- x13;

x10 + x12 - x14;

x15 - x17;

x16 - x18;

(x13 + x14) - x19;

(x17+x18) - x20];

I want to obtain the sensitivities of x1- x8 (which are my main variables) with changes in u1 and u2 which are my inputs and are constant values; (dy/du) using the finite differences method.

N.B: x9 - x20 are functions of x1 -x8, I have their equations solved and then substituted into the differential equation. I just need someone to help me with how to write the finite equations with changes in u rather than x as in the example above.

I hope my question is clear, I am still learning matlab.

thanks

[Wang Hong]

you can use symbolic expression to solve it