2.3 : The Product Rule

If functions f and g are diffrentiable at x

then so is f* g

Product rule

(fg)'=f'g + fg'

Product rule in words

derivqative of first times second + first times derivative of second

Leibniz notation of product rule:

d[f(x)g(x)]) / dx = f'(x)g(x) + f(x)g'(x)

Two ways to diffrentiate two simple binomials multiplied to each other

1. expand and use power rule
2. use product rule

derivative of position function gives

velocity function

if base is a polynomial

use chain rule

If the derivative is needed at a particular value:

it is not necessary to simplify before substituting