Let $X$ be a compact Riemann surface. Let $r(E), d(E)$ denote the rank and degree of a vector bundle $E$ on $X$.
From Narasimhan-Seshadri we have the following proposition
([Proposition 4.1) A vector bundle $W$ on $X$ is stable if for every proper subbundle $V$ of $W$, we have $d(W^*\otimes V)<0$.
The proof relies on this equality
$d(W^*\otimes V)=r(W)d(V) - r(V)d(W)$.
Where does the equality comes from?
Thank you.