  In this article, we investigate various numerical methods for computing
scaled or logarithmic sensitivities of the form $\partial \ln y/\partial \ln
x$. The methods tested include One Point, Two Point, Five Point, and the
Richardson Extrapolation. The different methods were applied to a variety of
mathematical functions as well as a reaction network model. The algorithms were
validated by comparing results with known analytical solutions for functions
and using the Reder method for computing the sensitivities in reaction networks
via the Tellurium package. For evaluation, two aspects were looked at, accuracy
and time taken to compute the sensitivities. Of the four methods, Richardson's
extrapolation was by far the most accurate but also the slowest in terms of
performance. For fast, reasonably accurate estimates, we recommend the
two-point method. For most other cases where the derivatives are changing
rapidly, the five-point method is a good choice, although it is three times
slower than the two-point method. For ultimate accuracy which would apply
particularly to very fast changing derivatives the Richardson method is without
doubt the best, but it is seven-times slower than the two point method. We do
not recommend the one-point method in any circumstance. The Python software
that was used in the study with documentation is available at:
\url{https://github.com/evanyfyip/SensitivityAnalysis}.
