Transversal intersection of graph and diagonal

Question

Suppose $f:\mathbb{R}^n \rightarrow \mathbb{R}^n$ is a smooth map. Let $$G=\{(x,y) \in \mathbb{R}^{2n}\ \mid y=f(x)\}$$ be the graph of $f$ and let $$D=\{(x,y) \in \mathbb{R}^{2n}\ \mid x=y\}$$ be the diagonal. My question is: when do $G$ and $D$ have a transverse intersection (as submanifolds of $\mathbb{R}^{2n}$)? I know that two submanifolds $N_1,N_2$ of $M$ have a transverse intersection if for every $p \in N_1 \cap N_2$, the tangent spaces $T_pN_1$ and $T_pN_2$ span $T_pM$. Now, in my case, the intersection is $$G \cap D=\{(x,x) \in \mathbb{R}^n\ \mid x=f(x)\},$$ the set of fixed points of $f$. I am not sure what to do next.