Deck 3: Section 5: Differentiation

Question 1

Find by implicit differentiation.

A)
B)
C)
D)
E)

Answer 1

Question 2

Find by implicit differentiation.

A)
B)
C)
D)
E)

Answer 2

Question 3

Use implicit differentiation to find an equation of the tangent line to the ellipse at .

A)
B)
C)
D)
E)

Answer 3

Question 4

Find by implicit differentiation given that . Use the original equation to simplify your answer.

A)
B)
C)
D)
E)

Question 5

Find by implicit differentiation.

A)
B)
C)
D)
E)

Question 6

Find the slope of the tangent line at the given point . Round your answer to two decimal places.

A) 0.67
B) 2.00
C) 1.00
D) 1.67
E) 3.00

Question 7

Evaluate for the equation at the given point . Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 8

Use implicit differentiation to find

A)
B)
C)
D)
E)

Question 9

Evaluate for the equation at the given point . Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 10

Find by implicit differentiation.

A)
B)
C)
D)
E)

Question 11

Find by implicit differentiation given that .

A)
B)
C)
D)
E)

Question 12

Find an equation of the tangent line to the graph of the function given below at the given point. (The coefficients below are given to two decimal places.)

A)
B)
C)
D)
E)

Question 13

Find by implicit differentiation.

A)
B)
C)
D)
E)

Question 14

Find an equation of the tangent line to the graph of the function at the point .The coefficients below are given to two decimal places.

A)
B)
C)
D)
E)

Question 15

Use implicit differentiation to find .

A)
B)
C)
D)
E)

Question 16

Find by implicit differentiation.

A)
B)
C)
D)
E)

Question 17

Find by implicit differentiation given that .

A)
B)
C)
D)
E)

Question 18

Evaluate for the equation at the given point . Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 19

Use implicit differentiation to find .

A)
B)
C)
D)
E)

Question 20

Use implicit differentiation to find at the point .

A)
B)
C)
D)
E)

Question 21

Differentiate with respect to t (x and y are functions of t).

A)
B)
C)
D)
E)

Question 22

Find the points at which the graph of the equation has a vertical or horizontal tangent line.

A) There is a vertical tangent at but no horizontal tangents.
B) There is a horizontal tangent at and a vertical tangent at .
C) There is a horizontal tangent at but no vertical tangents.
D) There is a horizontal tangent at and a vertical tangent at .
E) There are no horizontal or vertical tangent lines.

Question 23

Find in terms of x and y.

A)
B)
C)
D)
E)

Question 24

Find in terms of x and y.

A)
B)
C)
D)
E)

Question 25

Use logarithmic differentiation to find .

A)
B)
C)
D)
E)

Question 26

Use logarithmic differentiation to find the derivative of .

A)
B)
C)
D)
E)

Question 27

Find in terms of x and y given that . Use the original equation to simplify your answer.

A)
B)
C)
D)
E)

Question 28

Use logarithmic differentiation to find .

A)
B)
C)
D)
E)

Question 29

Find in terms of x and y given that

A)
B)
C)
D)
E)

Question 30

Differentiate with respect to t (x and y are functions of t).

A)
B)
C)
D)
E)