I premise that I'm very new to the study of algebraic geometry so probably things that can look trivial are not so clear to me.
Let $f : X \rightarrow Y$, $g: Y\rightarrow Z$ be morphisms of schemes.
My goal is to show that this sequence is exact:
$ f^*\Omega_{Y/Z} \longrightarrow \Omega_{X/Z} \longrightarrow \Omega_{X/Y} \longrightarrow 0$
I read everywhere that I have to use the first fundamental exact sequence, i.e.:
$ \Omega_{B/A} \bigotimes_{B} C \longrightarrow \Omega_{C/A} \longrightarrow \Omega_{C/B} \longrightarrow 0 $
where $ A \longrightarrow B \longrightarrow C $ are morphisms of $A$-algebras.
Now, the first problem is that I'm not able to use the definition of the pullback in such a way to explicit the correct tensor product.
The second problem is that, even solving the first, it seems to me that the two sequences don't fit ( $A,B,C$ don't correspond to $X,Y,Z$) in the two sequences.