Review Sheet for CP Calculus Quiz 2-3 and 2-4

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u = v = u’ = v’ =

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Review Sheet for CP Calculus Quiz 2-3 and 2-4

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!)

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