Answer
$f_{R_1}=-R_1^{-2}$
$f_{R_2}=-R_2^{-2}$
$f_{R_3}=-R_3^{-2}$
Work Step by Step
Rewrite the equation: $f(R_1, R_2, R_3)=R_1^{-1}+R_2^{-1}+R_3^{-1}$
Take the first partial derivatives of the given function. When taking partial derivative with respect to $R_1$, treat $R_2$ and $R_3$ as constants. Use this same method when taking partial derivative with respect to $R_2$ and $R_3$:
$f_{R_1}=-R_1^{-2}+0+0=-R_1^{-2}$
$f_{R_2}=0-R_2^{-2}+0=-R_2^{-2}$
$f_{R_3}=0+0-R_3^{-2}=-R_3^{-2}$
