Answer
$R_p=\frac{q^2}{p^2q^4+1}$, $R_q=\frac{2pq}{p^2q^4+1}$.
Work Step by Step
$R(p,q)=\arctan{(pq^2)}$
In order to find $R_p$ we treat $q$ as a constant and differentiate with respect to $p$.
$R_p=\frac{q^2}{p^2q^4+1}$
In order to find $R_q$ we treat $p$ as a constant and differentiate with respect to $q$.
$R_q=\frac{2pq}{p^2q^4+1}$
