We generalize the combinatorial identity for binomial coefficients underlying the construction of Pascal's Triangle to multinomial coefficients underlying the construction of Pascal's Simplex. Using this identity, we present a new proof of the formula for calculating the nth derivative of the product of k functions, a generalization of Leibniz's Rule for differentiation.

Author Bio

As an undergraduate majoring in mathematics-statistics, economics, and political science at the University of Connecticut, Rajeshwari started working on this research project after taking classes in advanced calculus and probability. While she plans to pursue a research career in economics after graduating from UConn in 2018, she has very broad interests in the mathematical sciences, fueled by her participation in REU programs in 2015, 2016, and 2017 in the areas of stochastic differential equations, data science, and stochastic finance and random matrices, respectively. She has also engaged in supervised and collaborative research in diverse topics in mathematical statistics, including time series analysis, asymptotic distribution theory, and multivariate analysis.