A new approach to differentiation on a time scale is presented. We give a suitable generalization of the Vitali Lemma and apply it to prove that every increasing function f: → ℝ has a right derivative f₊’(x) for ${\mu }_{\Delta }$-almost all x ∈ . Moreover, ${\int }_{[a,b)}f{₊}^{\text{'}}\left(x\right)d{\mu }_{\Delta }\le f\left(b\right)-f\left(a\right)$.