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.
"Generalization of Pascal's Rule and Leibniz's Rule for Differentiation,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18:
1, Article 12.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/12