The bivariate Student t copula is a mathematical function that allows for the modeling of dependence between two random variables. It is derived from the multivariate Student t distribution, which incorporates heavy tails and allows for capturing extreme observations. The copula function itself represents the dependence structure between the variables, separate from their marginal distributions. By utilizing the bivariate Student t copula, one can assess the joint behavior of the variables and calculate partial derivatives with respect to specific parameters. These derivatives can provide valuable insights into the sensitivity and relationship between variables in a given model or analysis.