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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!)*