Which of the following carboxylic acid derivatives is the most reactive towards nucleophilic acyl substitution?

Reactivity follows the leaving-group ability, i.e. the weakness of the conjugate base: $\mathrm{Cl}{}^{-}$ (from HCl) is the weakest base. The order is acid chloride $>$ anhydride $>$ ester $>$ amide, so $\mathrm{CH}{}_3-\mathrm{COCl}$ is the most reactive.