Analytical expressions are found for the derivatives of commonly used Mie scattering parameters, in particular the absorption and the scattering efficiencies, and for the angular intensity functions. These expressions are based on the analytical derivatives of the Mie scattering amplitudes a(n) and b(n) with respect to the particle size parameter and complex refractive index. In addition, analytical derivatives are found for the volume absorption and scattering coefficients, as well as for the intensity functions of a population of particles with log normal size distribution. These derivatives are given with respect to the total number density, to the median radius and spread of the distribution, and to the refractive index. Comparison between analytically and numerically computed derivatives showed the analytical version to be 2.5 to 6.5 times as fast for the single-particle and particle-distribution cases, respectively.