3.2 The Product and Quotient Rules The Product Rule The Quotient Rule

3.2 Using the Product & Quotient Rules Find the derivative of each function. F(x)=(3x2+4) (x3-2) 3. 4.

3.2 Application Example Worldwide sales, in millions of dollars, of a DVD recording of a hit movie t months from the date of release is given by Find the rate at which sales are changing at time t. How fast are sales changing: At the time the DVD is released (t=0)? Six months from the date of release? Answer in complete sentences.

3.3 The Chain Rule Algebra review. In composition of functions: the output of one function is used as input to another function; there is an inside function and an outside function. If f(x)=x2 and g(x)=5x+1, then Note the answer to the first example above is a function raised to a power. Whenever you have a function raised to a power, like this example, you can think of composition and a function inside of a function.

3.3 The Chain Rule If h(x)=g[f(x)], so g is the outside function and f is the inside function, then the derivative of h equals the derivative of the outside function g at the inside function f times the derivative of the inside function f. In symbols, h’(x)=g’[f(x)] f ’(x) General Power Rule (special case of chain rule) {[f(x)]n}’=n[f(x)]n-1 f ’(x)

3.3 Using the Chain Rule/General Power Rule Find the derivative of each function. 1. f(x)=(3x+1)5 2. 3. 4.