  We trace derivations through Demazure's correspondence between a finitely
generated positively graded normal $k$-algebras $A$ and normal projective
$k$-varieties $X$ equipped with an ample $\mathbb{Q}$-Cartier
$\mathbb{Q}$-divisor $D$. We obtain a generalized Euler sequence involving a
sheaf on $X$ whose space of global sections consists of all homogeneous
$k$-linear derivations of $A$ and a sheaf of logarithmic derivations on $X$.
