u = v = u’ = v’ =
Name:
1. Write out the Power Rule.
(You will need to know this on the quiz – it will not be given to you!)
2. Write out the Product Rule.
(You will need to know this on the quiz – it will not be given to you!)
3. Write out the Quotient Rule.
(You will need to know this on the quiz – it will not be given to you!)
4. Write out the Chain Rule.
(You will need to know this on the quiz – it will not be given to you!)
5. Use the Power Rule to find the derivative of
y

5
x
5

2
x
4

7
x
2
x x to re-write this function first so everything is to a power!)
6. Use the Product Rule to find f ’(x) when f(x) = (3
x
2
 
1)(5
x
3

2
x
2

7)
2
3
x
6

3
x
2
(Hint- you need

7. Use the Quotient Rule to find
dy dx
if
y

5
x
2
2
x

2
x

1 u = v = u’ = v’ =
8. Use the Chain Rule to find the derivative of

(2
x
3
1)
5
(Hint- derivative of the inside = ?)
9. Use the Product Rule (and the Chain Rule!) to find the derivative of

(
x
3
x x

3)

10. Find
dy dx
if
y

8
x

x

x
2
)
11. Suppose
f
and
g
are functions with values f (3) = 2, g (3) = -10, f ‘(3) = -1, and g‘(3) = 7. a. Find (
f

g
) '(3) b. Find (
g
 c. Find (
fg
) '(3)
(Hint- Product Rule!)
d. Find
g
'
(3)
(Hint- Quotient Rule!)
12. Find the derivative of f(x) =



4
x
3

5
3
x
7



5
(Think about what rule and re-writing!)

13. What is the derivative of f(x) = |x|? Explain. What would it look like as a piecewise function??
f
 

14. Use implicit differentiation to find the derivative if 4
x
2

y
2

9
15. Use implicit differentiation to find the equation of the tangent line for the equation from #14 at the point (1, -1).

Extra Practice!
1. Use implicit differentiation on the equation
 
x
2

3
to find
dy dx
and the equation for a tangent line at the point (-3, 1).
2. Use the Quotient Rule (and the Chain Rule!) to find the derivative of
y

(2
x
(3
x
2


3)
7)
2
3. Find the derivative of

(2
x
2

5
x

x
2

2)
2
4. Find
dy dx
if
y

(9

x
2 3
)
8
x
5. Find the derivative of f(x) =
4
x
3

5
3
x
7

6. Use implicit differentiation to the tangent line of
y
6

3
x
0 at the point (1, 1).
7. Suppose
f
and
g
are functions with values f (3) = 6, g (3) = 3, f ‘(3) = -8, and g‘(3) = 1. a. Find (
f

g
) '(3) b. Find (
g
 c. Find (
fg
) '(3)
(Hint- Product Rule!)
d. Find
g
'
(3)
(Hint- Quotient Rule!)