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 to re-write this function first so everything is to a power!) y

5 x 5 
2 x 4 
7 x 2 x
1 2 x 3 x 6
 3 x 2
(Hint- you need
6. Use the Product Rule to find f ’(x) when f(x) = (3 x
2  
1)(5 x
3 
2 x
2 
7)

7. Use the Quotient Rule to find dy dx
if y

5 x
2 
2
2 x

1 x u = v = u’ = v’ =
8. Use the Chain Rule to find the derivative of ( )

(2 x
3 x 1)
5
(Hint- derivative of the inside = ?)
9. Use the Product Rule (and the Chain Rule!) to find the derivative of f x

( x
3
3 x 1) (2 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

3 ) '(3) 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 y
 y x
 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
2 
3)
2
(3 x

7)
3. Find the derivative of f x

(2 x
2 
5 x

7) ( x
2 
2)
2
4. Find dy dx
if y

 x
2 3
(9 )
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 4 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

3 ) '(3) c. Find ( fg ) '(3) (Hint- Product Rule!) d. Find g
'
(3)
(Hint- Quotient Rule!)