Section 3.3 The Product and Quotient Rule

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

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”

Examples

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

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

Examples