Answer
$\displaystyle \frac{\partial R}{\partial R_{1}}=\frac{R^{2}}{R_{1}^{2}}$
Work Step by Step
Apply $\displaystyle \frac{\partial}{\partial R_{1}}$ to both sides.
LHS: R is a function of $R_{1}.$ (chain rule)
RHS: $R_{2},$ and $R_{3}$ are threated as constants.
$\displaystyle \frac{\partial}{\partial R_{1}}[R^{-1}]=\frac{\partial}{\partial R_{1}}[R_{1}^{-1}]+0+0$
$-R^{-2}\displaystyle \cdot\frac{\partial R}{\partial R_{1}}=-R_{1}^{-2}$
$\displaystyle \frac{\partial R}{\partial R_{1}}=\frac{R^{2}}{R_{1}^{2}}$
