We prove a p-adic, local version of the Monotonicity Theorem forP-minimal structures. The existence of such a theorem wasoriginally conjectured by Haskell and Macpherson. We approach the problem byconsidering the first order strict derivative. In particular, we show that, fora wide class of P-minimal structures, the definable functionsf : K → K arealmost everywhere strictly differentiable and satisfy the Local JacobianProperty.