SECTION 3.4: The Product and Quotients Rule

The Product Rule:

If u = f(x) and v= g(x), and they are both differential functions then

(fg)' = f ' g + g ' f

It can also be written as :

d (uv)/ dx = (du/dx)*v + (dv/dx)*u

It is to be noted that the derivative of a product is not simply the product of the derivatives of the two functions involved. 

The Quotient Rule:

If u = f(x) and v = g(x)

then (f/g) ' = (f ' g - g ' f)/ g^2

It can also be written as d/dx(u/v) = ((du/dx)*v - (dv/dx)*u)/(v^2)

The difficulty in understanding this section lies in the usage of the quotient rule and how it was derived as essentially the function could simply be converted into a product rather than a quotient.

Derivatives continue to be important in analyzing smaller and smaller everyday changes. For this reason, both the product rule and the quotient rule serve to simplify the understanding of derivatives in everyday applicability.