Differentiation: (lesson 2 of 3)

## Product and Quotient Rule for Derivatives

### Product Rule

Let f(x) and g(x) be differentiable at x.
Then h(x) = f(x)g(x) is differentiable at x and

We illustrate product rule with the following examples:

Example 1:

Example 2:

### Quotient rule:

Let f(x) and g(x) be differentiable at x with
g(x) ≠ 0 . Then f(x)/g(x) is differentiable at x and

We illustrate quotient rule with the following examples:

Example 3:Differentiate

Solution 3:

Example 4:Differentiate

Solution 4:

Example 5:Differentiate

Solution 5:

## Random Quote

I am ever more convinced that the necessity of our geometry cannot be proved -- at least not by human reason for human reason.

Carl Friedrich Gauss

## Random Quote

A mathematician is a device for turning coffee into theorems.

Paul Erdos