Sensitivity analysis covers a lot of different things. Then, since you are a programmer, let me suppose that you make a call to a function $F(a,b,x)$ which returns to your program the profit $P_0$ of a plant running at operating conditions $a$ and $b$. Now, change your first set point to $(a+\Delta a)$ and $b$ al call $F(a+\Delta a,b,x)$ to get $P_1$. This gives you the sensitivity of the profit to the first set point value. This looks like derivatives, isn't ?
< is a good and simple view of it and I just quote the beginning of what they write
> Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs.