Use distribution or FOIL first, then find the derivative. 1. Find f'(x) if f(x) = 9x3(2x2 - 7). 2. Find a [(x - 12) (x2 +3)]. dx Use the PRODUCT RULE to find the derivative. 3. Find f'(x) if f(x) = 9x3(2x2 - 7). 4. Find " [(x - 12 ) (x2 + 3)]. dx2. Examples of finding the derivative using the product rule. a. Here is the product rule. (f (x) . g(x)>' = f(x)g'(x) + f'(x)g(x). b. Written example. h(x) =(x3 - 3)(x2+2). Find h'(x) 1. Using the product rule we will evaluate the derivative. h' (x) = (x3 - 3) - [(x2 + 2)]+ -[(x3 - 3)](x2+2) Hence, this is the derivative. h'(x) = (x3 -3)(2x)+3x2(x2+2) We can simplify the derivative and compare it to what we found it in the previous page. h'(x) =2x4-6x+3x4+6x2=5x4+6x2-6x Previous page with same results. dx f' (x) = [(x3 - 3)(x2 + 2)]= (x5+2x3-3x2-6)=5x4+6x2-6x dx\fD Question 1 7 pts Use the product rule to evaluate. ( x 2 ( x - 3) ) dx D Question 2 8 pts Use the quotient rule to evaluate. (x+2 O 3x2 1 - =3x2 O 2 x3 + 6 x2 ( x + 2) 2 0 -2x3- 6x2 ( x + 2) 2 O 8x5 ( x + 2)2