Home > RHUMJ > Vol. 18 (2017) > Iss. 1

#### Abstract

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 *n*^{th} derivative of the product of *k* functions, a generalization of Leibniz's Rule for differentiation.

#### Recommended Citation

Majumdar, Rajeshwari
(2017)
"Generalization of Pascal's Rule and Leibniz's Rule for Differentiation,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 18
:
Iss.
1
, Article 12.

Available at:
http://scholar.rose-hulman.edu/rhumj/vol18/iss1/12