Ext group as derived functor of Hom

Question

I am familiar with the definition $\operatorname{Ext} _\mathcal{A}^k\left( {M,N} \right) = \left( {{R^k}{{\operatorname{Hom} }_\mathcal{A}}\left( {M, - } \right)} \right)\left( N \right)$, the derived functor of the left exact functor $\operatorname{Hom}(M,-)$. But I was wondering what is $$ \left( {{R^k}{{\operatorname{Hom} }_\mathcal{A}}\left( {-, N } \right)} \right)\left( M \right) $$ the derived functor of the left exact functor $\operatorname{Hom}(-,N)$. What's the relation between the two different derived functors?