We consider random variables of the form F=f(V1,...,Vn) where f is a smooth function and V_i,i\in\mathbbN are random variables with absolutely continuous law pi(y). We assume that pi,i=1,...,n are piecewise differentiable and we develop a differential calculus of Malliavin type based on \partial\lnp_i. This allows us to establish an integration by parts formula E(∂iϕ(F)G)=E(ϕ(F)Hi(F,G)) where Hi(F,G) is a random variable constructed using the differential operators acting on F and G. We use this formula in order to give numerical algorithms for sensitivity computations in a model driven by a Lévy process