One of the Leibniz Rules One of several Leibniz Rules in calculus deals with higher-order...

One of the Leibniz Rules One of several Leibniz Rules in calculus deals with higher-order derivatives of products. Let (fg)(n) denote the nth derivative of the product fg, for n ≥ 1.

a. Prove that (fg)(2) = f″g + 2f′g′ + fg″.

b. Prove that, in general,

,

where  are the binomial coefficients.

c. Compare the result of (b) to the expansion of (a + b)n.