We prove a p-adic, local version of the Monotonicity Theorem for
P-minimal structures. The existence of such a theorem was
originally conjectured by Haskell and Macpherson. We approach the problem by
considering the first order strict derivative. In particular, we show that, for
a wide class of P-minimal structures, the definable functions
f : K → K are
almost everywhere strictly differentiable and satisfy the Local Jacobian
Property.