In this talk I will show that if $C^*_u(X)$ is a uniform Roe algebra associated to a bounded geometry metric space $X$, then all bounded derivations from $C^*_u(X)$ to itself are inner. We obtain this result using a ``reduction of cocycles" method from Sinclair and Smith. Then the key technical ingredient comes from recent work of Braga and Farah in their paper ``On the Rigidity of Uniform Roe Algebras".