Monopolies are just a mathematical misunderstanding
$PQ(P)=TR$, Total Revenue. 

$\frac{∂Q}{∂P}P+Q$ is the derivative of $PQ(P)$ with respect to $P$.

$MR$, Marginal Revenue, is the derivative of $TR$ with respect to $Q$.

So in general $\frac{∂Q}{∂P}P+Q \neq MR$