Calculates the partial derivative of the first-passage time diffusion probability density function (PDF) and cumulative distribution function (CDF) with respect to the first-passage time t (only for PDF), the upper barrier a, the drift rate v, the relative starting point w, the non-decision time t0, the inter-trial variability of the drift rate sv, the inter-trial variability of the rel. starting point sw, and the inter-trial variability of the non-decision time st0. In addition the PDF and CDF themselves are also provided. Most calculations are done on the logarithmic scale to make it more stable. Since the PDF, CDF, and their derivatives are represented as infinite series, we give the user the option to control the approximation errors with the argument 'precision'. For the numerical integration we used the C library cubature by Johnson, S. G. (2005-2013) < https://github.com/stevengj/cubature>. Numerical integration is required whenever sv, sw, and/or st0 is not zero. Note that numerical integration reduces speed of the computation and the precision cannot be guaranteed anymore. Therefore, whenever numerical integration is used an estimate of the approximation error is provided in the output list.