Explore the Calculus of n^th Derivatives

The sum, product and chain rules for derivatives can be generalized to the case of ^th derivatives, as illustrated in the following.

The ^th derivative of a sum is the sum of the ^th derivatives.

The ^th derivative of a product is given by the Leibniz rule.

Make a table that shows the product rule for 1, 2, 3.

The ^th derivative of a composition is given by the chain rule.

Make a table that shows the chain rule for 1, 2, 3.