All the derivatives shown are derived from the carboxylic acid shown. Which derivative is hydrolysed fastest by cold water?

The rate of nucleophilic acyl substitution follows the leaving group ability: $\mathrm{Cl}{}^{-}>$ carboxylate $>$ alkoxide $>$ amide ion. Ethanoyl chloride therefore hydrolyses fastest, then the anhydride, then the ester, while ethanamide is hydrolysed only on prolonged heating with acid or base.