# What does differentiability of Utility function at an optimal solution x* mean?

I am working with Rubinstein's book. It states there that if preferences are differentiable, then value per dollar at a bundle of a commodity is as large as value per dollar of the bundle of any other commodity.

Then we are given that if preferences are represented by a Utility function that is differentiable at x* (optimal solution) then $$D_k U(x*)/ p_k ≥ D_i U(x*)/ p_i$$.

I do not understand the mathematical part of the definition. X* is an optimal solution (bundle of $$x_k$$ and $$x_j$$ commodities). They are both in the bundle so why would the value per dollar of $$x_k$$ be higher than value per dollar of $$x_j$$?