Answer
$-R_1^{-2},-R_2^{-2}, -R_3^{-2} $
Work Step by Step
Given: $f=R_1^{-1}+R_2^{-1}+R_3^{-1}$
Now, $\dfrac{\partial f}{\partial R_1}=\dfrac{\partial }{\partial R_1} [R_1^{-1}+R_2^{-1}+R_3^{-1}]=-R_1^{-1-1}=-R_1^{-2}$
and
$\dfrac{\partial f}{\partial R_2}=\dfrac{\partial }{\partial R_2} [R_1^{-1}+R_2^{-1}+R_3^{-1}]=-R_2^{-1-1}=-R_2^{-2}$
and
$\dfrac{\partial f}{\partial R_3}=\dfrac{\partial }{\partial R_3} [R_1^{-1}+R_2^{-1}+R_3^{-1}]=-R_3^{-1-1}=-R_3^{-2}$
Hence, $-R_1^{-2},-R_2^{-2}, -R_3^{-2} $
