Principal Component Analysis (PCA) is a promising tool for enhancing radiative transfer (RT) performance. When applied to binned optical property data sets, PCA exploits redundancy in the optical data, and restricts the number of full multiple-scatter calculations to those optical states corresponding to the most important principal components, yet still maintaining high accuracy in the radiance approximations. We show that the entire PCA RT enhancement process is analytically differentiable with respect to any atmospheric or surface parameter, thus allowing for accurate and fast approximations of Jacobian matrices, in addition to radiances. This linearization greatly extends the power and scope of the PCA method to many remote sensing retrieval applications and sensitivity studies. In the first example, we examine accuracy for PCA-derived UV-backscatter radiance and Jacobian fields over a 290-340. nm window. In a second application, we show that performance for UV-based total ozone column retrieval is considerably improved without compromising the accuracy.