This paper presents an efficient method to analyze variations that nuclear data perturbations induce in one-dimensional power-density distributions. This method is called the Taylor-generalized perturbation theory (Taylor-GPT) method since it is based on (a) use of a Taylor series expansion of the response variation, and (b) use of generalized perturbation theory (GPT) to evaluate the derivative operators that appear as coefficients in this Taylor series. Equations satisfied by the importance functions for the derivatives of the response variations are derived and solved with existing GPT codes. The characteristics of these functions are highlighted analytically. Particular attention is focused on the numerical value and location of the maximum power density. This is because perturbations in system parameters affect not only the value at the maximum, but also the location of this maximum. The Taylor-GPT method can efficiently assess such effects. The practical usefulness of the Taylor-GPT method is illustrated by considering test cases involving a simplified heterogeneous liquid-metal fast breeder reactor model. The results indicate that this method is as accurate as the GPT method, yet requires fewer calculations when investigating space-dependent power density variations.