Partial differentiation for parallel Resistance Problem

Question

I have this solved problem , and is not clear for me how the teacher got the result. I tried doing someting on the right side of the picture, but i am not sure is correct ... I wonder if someone can show me step by step

Answer 1

$$R_T^{-1}=R_1^{-1}+R_2^{-1}+R_3^{-1}.$$

Take the partial derivative on $R_1$ and get

$$-R_T^{-2}\frac{\partial R_T}{\partial R_1}=-R_1^{-2}$$ or

$$\frac{\partial R_T}{\partial R_1}=\frac{R_T^2}{R_1^2}$$ and similarly for the other resistances.

Then

$$\Delta R_T\approx \frac{R_T^2}{R_1^2}\Delta R_1+\frac{R_T^2}{R_2^2}\Delta R_2+\frac{R_T^2}{R_3^2}\Delta R_3.$$