1. 3-3 rules for differentiation

2. (1) Derivative of a Constant EX:
For the following rules, c = constant, u = function, v = function
(1) Derivative of a Constant
EX:
y = c is a horizontal line  slope ALWAYS 0!
(2) Positive Integer Powers of x
EX:
(nickname: “pop & drop”)
the # in front
power by 1

3. Constant times deriv of function
For the following rules, c = constant, u = function, v = function
(3) Constant Multiple
EX:
function
Constant times deriv of function
(4) Sum and Difference Rule
EX:

4. It’s ok that they are different letters
Ex 1)
It’s ok that they are different letters
Ex 2) Does the curve y = x4 – 2x2 + 2 have any horizontal
tangents? If so, where?
* horizontal tangent… m = 0
*use orig function to find
y-values of points
Yes, at (0, 2), (–1, 1), and (1, 1)

5. Ex 3) Using our calculators, find where the graph of
y = 0.2x4 – 0.7x3 – 2x2 + 5x + 4 has horizontal tangents.
Use 2nd CALC
 2:zero
x  –1.862, 0.948, and 3.539
(5) Product Rule
1st times deriv of 2nd plus 2nd times deriv of 1st
Ex 4)

6. (6) Quotient Rule
*bottom times deriv of top MINUS top times deriv of bottom ALL OVER bottom squared
Ex 5)
*don’t need to simplify!

7. (*super popular on AP exam!)
Ex 6) Let y = uv be the product of the functions u and v.
Find y'(2) if u(2) = 3, u'(2) = –4, v(2) = 1, and v'(2) = 2
(7) Negative Integer Powers of x
(nickname: pop & drop)
(same as positive powers )

8. Ex 7) Find an equation for the line tangent to the curve
*might be easier to separate instead of quotient rule
 slope
y – 2 = –1(x – 1)

9. Higher Order Derivatives
Ex 8) Find the first four derivatives of y = x3 – 5x2 + 2

10. homework
Worksheet 3-3