Let $q$ be a power of a prime $p$ and $P$ be an irreducible polynomial of $\mathbb F_q[T]$. Denote by $\mathbb C_P$ the completion of an algebraic closure of $\mathbb F_q(T)$ for the normalized valuation $v_P$ ($v_P(P)=1$) Denote by $K_P$ the separable closure of $\mathbb F_q(T)$ in $\mathbb C_P$. One knows that the derivative on $\mathbb F_q(T)$ can be extended uniquely in $K_P$ (one still denotes it by $'$). My question: for every $\alpha\in K_P$, does one have $v_P(\alpha')=v_P(\alpha)-1$ or $v_P(\alpha')\ge v_P(\alpha)$. Obviously, it is true for $\alpha\in\mathbb F_q(T)$.