Derivative of an \( (M,n,p) \)-Function
Let \(f:\mathbb{F}_{p^m} \rightarrow \mathbb{F}_{p^n}\) be an \((m,n,p)\)-function , and take \(a \in \mathbb{F}_{p^m}\). The derivative of \(f\) in the direction of \(a\) is defined to be:
\[ D_a{f(x)}=f(x+a)-f(x) \]