A new derivation of the perturbation operator used in the MCNP radiation transport code is presented, and equations are determined to evaluate the change in the response from a perturbation in macroscopic cross section due to the first, second, third, and fourth derivative terms, and the second-derivative cross term. The perturbation operator in MCNP currently can be used to determine the change in a response from the first and second order terms in Taylor expansion due to such a perturbation. The derivation presented here produces expressions that are equivalent to the expressions used in MCNP for the first and second derivative, but are simpler and are in a form that more readily reveals their physical significance. The perturbation operator is particularly useful for sensitivity and uncertainty analysis.