1. Section 3.3 The Product and Quotient Rule

2. So if f and g are differentiable functions we have (fg)’ ≠ f’g’
Consider the function
What is its derivative?
What if we rewrite it as a product
Now what is the derivative?
So if f and g are differentiable functions we have (fg)’ ≠ f’g’
Thus we come to another rule

3. Theorem 3.3: Product Rule
If u = f(x) and v = g(x) are differentiable, then
(fg)’ = f ’g + f g’
The product rule can also be written
“The derivative of the product is the derivative of the first times the second plus the derivative of the second times the first”

4. Examples

5. Just like with products, we have a similar rule for quotients
In fact we can derive the rule from our product rule

6. Section 3.4: Quotient Rule
If u = f(x) and v = g(x) are differentiable, then
The quotient rule can also be written

7. Examples