How to calculate an error in a function?

Question

I have this function : T= (R1+R2-R12)/(2*R1*R2) and I want to calculate the error in T? So What is the general principle in calculating the error or uncertainty in a function of several variables ?

Answer 1

In your case, you have to use logarithmic derivative.

$\frac{dT}{T}=\frac{d(R_1+R_2+R_3)}{R_1+R_2+R_3}-\frac{dR_1}{R_1}-\frac{dR_2}{R_2}$

which gives the relative error

$dT=T.( \frac{dR_1+dR_2+dR_3}{R_1+R_2+R_3}-\frac{ dR_1}{R_1}-\frac{ dR_2}{R_2})$

then you replace for example $dR_1$ by your error at $R_1$, $\delta R_1$ and signum $-$ by $+$ to obtain an upper bound.