What is the meaning of product rule?

The product rule is a formula that is used to find the derivative of the product of two or more functions.

It is summarized as thus: y' = u x v' + v x u' ("first times the derivative of the second, plus the second times the derivative of the first").

Ex:

y = (2x4 + 6x3 + 9x) X (3x2 + x7+ 12)

y' = (2x4 + 6x3 + 9x) X (6x + 7x6) + (3x2 + x7+ 12) X (8x3 + 18x2 + 9)

y' = 12x5 + 14x10 + 36x4 + 54x2 + 63x7 + 24x5 + 54x4 + 27x2 + 8x10 + 18x9 + 9x7 + 96x3 + 216x2 + 108

y' = 36x5 + 22x10 + 90x4 + 297x2 + 72x7 + 18x9 + 96x3 + 108