[Physics] Relative error of equivalent resistance of resistors in parallel

Question

I just saw a formula in my book for relative error in equivalent resistance of two resistors connected in parallel.

$\frac{\Delta R}{R^2} = \frac{\Delta R_1}{R_1^2}+\frac{\Delta R_2}{R_2^2}$

How do I derive this formula?

Answer 1

Start with

$\frac{1}{R} = \frac{1}{R_1}+\frac{1}{R_2}$ for paralllel resistors

Then apply equation 4a from this reference to each side. In other words, consider the right side as $f(R_1, R_2)$ and the left side as $f(R)$.

$\Delta f(R) = \Delta f(R_1, R_2)$