Deck 13: Additional Differentiation Topics

Question 1

Find y' if y =
(4x + 5).

Answer 1

or

Question 2

Find y' if y = ln
.

Answer 2

-

Question 3

Find y' if y =
.

Answer 3

Question 4

Find y' if y = ln(
- 3).

Question 5

Find y' if y =
.

Question 6

Find y' if y = ln
.

Question 7

If y =
,then find y'.

Question 8

Find
where y =
(
+ 3x + 1).

Question 9

Find y' if y = ln(
)+
x.

Question 10

Find y' if y =
.

Question 11

If y = ln
,then find
.

Question 12

Find y' if y =
ln(4x + 5).

Question 13

If y = ln ,then y' =

A)
B)
C)
D)
E)

Question 14

If y =
,then find y'.

Question 15

If y = ln ,then
=

A) -
B)
C)
D)
E)

Question 16

Find y' if y = ln
.

Question 17

Find
where y = ln
.

Question 18

If y = (ln ,then
=

A) 0.
B) 2 ln 2.
C)
D)
E)

Question 19

Find y' if y = log
.

Question 20

Find an equation of the tangent line to the curve y = ln(x + 3)when x = -2.

Question 21

At a soccer game concession stand,the profit P from selling x number of T-shirts (in hundreds)is given by
Find
.

Question 22

Suppose that the supply of q units of a product at price $p is given by q = 10 + 25 ln p.Find
.

Question 23

Find y' if y =
.

Question 24

A shoe company is planning a new brand of walking shoe for the market.Research shows that x,the number of shoes sold (in thousands)at a price of $p,can be approximated by x = -2ln
where
Find
.

Question 25

In psychology,the Weber-Fechner law for stimulus response is R = k ln
where R is the response,S is the stimulus,and
is the lowest level of stimulus that can be detected.Find
.

Question 26

The total revenue from the sales of a certain product are given by
Find the marginal revenue.

Question 27

The Reynolds number is a quantity that relates to the flow of a liquid.If it is given by the equation
where x is the radius of the tube the liquid flows through and A and B are positive constants,find
.

Question 28

If y = f(x)=
,find the (a)relative and (b)percentage rate of change of y when x = 0.5.

Question 29

Find y' if y =
.

Question 30

The total revenue from the sales of a certain product are given by R(x)=
.Find the marginal revenue.

Question 31

The intensity of an earthquake is measured on the Richter scale.The reading R is given by R = log
,where I is the intensity and
is a standard minimum intensity.If
= 5,find
,the rate of change of the Richter scale reading with respect to the intensity.

Question 32

The total revenue from the sales of a certain product are given by R(x)=
.Find the marginal revenue.

Question 33

Find y' if y =
.

Question 34

An experiment was set up to find a relationship between weight and systolic blood pressure in children.It was found that p(x),the systolic blood pressure,was approximately p(x)= 17.5(1 + ln x),where x is the child's weight in pounds.Find p'(x).

Question 35

At a football game concession stand,the profit P from selling x number of T-shirts (in hundreds)is given by
Find
.Use your graphing calculator to graph both P and
on the same set of axes.Verify that when the graph of P reaches its peak,the graph of
crosses the x-axis.

Question 36

If p =
,find the rate of change of p with respect to q when q = 2.

Question 37

At a volleyball game concession stand,the profit P from selling x number of T-shirts (in hundreds)is given by P = 8x - 4x ln x.Find
.Use your graphing calculator to graph both P and
on the same set of axes.Verify that when the graph of P reaches its peak,the graph of
crosses the x-axis.

Question 38

The total revenue from the sales of a certain product are given by R(x)=
.Find the marginal revenue.

Question 39

Find y' if y =
.

Question 40

The loudness of sound (L,measured in decibels)perceived by the human ear depends upon intensity levels (I)according to L = 10 log
,where
is the standard threshold of audibility.If
= 1,find
,the rate of change of the loudness with respect to the standard threshold of audibility.

Question 41

If y = e
,then find y'.

Question 42

If y =
×
,then find y'.

Question 43

If y =
,then find y'.

Question 44

If f(x)= ,then f'(x)=

A)
B)
C)
D)
E)

Question 45

Suppose the demand equation for the manufacturer's product is p = 100
,where p is the price per unit for q units.Find the marginal revenue function.

Question 46

Suppose a population is growing according to the equation P =
.Find the rate of growth of the population,
.

Question 47

Find y' if y =
.

Question 48

If y = ( + 5x - 1)
,then y' =

A) (2x + 5)
B) ( + 7x + 4)
C)
D) (2 + 12x + 3)
E) (3 - 10x + 7)

Question 49

If y =
,then find y'.

Question 50

Find y' if y =
.

Question 51

Suppose a population is growing according to the equation P =
.Find the rate of growth of the population,
.

Question 52

Suppose a population is growing according to the equation P =
.Find the rate of growth of the population,
.

Question 53

Find y' if y =

.

Question 54

The percentage p of a certain radioactive element present after t years is given by p =
.Find
.

Question 55

The average cost for producing q units of product is given by
=
)At a production level of 900 units,the marginal cost is

A)
B)
C) 0.87.
D) 0.87e.
E)

Question 56

If f(x)= ,then f'(x)=

A)
B)
C) (4x + 1)
D) 2(4x + 1)
E) 8(4x + 1)

Question 57

Suppose a population is growing according to the equation P =
.Find the rate of growth of the population,
.

Question 58

Medical research has found that between heartbeats the pressure in the aorta of a normal adult is a function of time and can be modeled by the equation P = 95
.Find
,the rate at which the pressure changes with respect to time.

Question 59

Find y' if y =
.

Question 60

If y =
+
,then find y'.

Question 61

If the demand equation for a product is q =
,where q is the number of units demanded at price p per unit,find the elasticity of demand when p = 48.

Question 62

Differentiate: g(x)= 4x

Question 63

Differentiate: f(x)=

Question 64

The percentage p of a certain radioactive element present after t years is given by p =
.Find
.

Question 65

Differentiate: f(x)=

Question 66

If the point elasticity of demand for a product is -2.3 and the price of the product increases 3%,what is the approximate percentage decrease in demand?

Question 67

Differentiate: h(x)=

Question 68

The demand function for a manufacturer's product is given by p =
,where p is the price per unit when q units are demanded.
(a)Find the point elasticity of demand when q = 100.
(b)For q = 100,is demand elastic,inelastic,or does it have unit elasticity?

Question 69

The demand function for a manufacturer's product is given by p = 20 - 0.02q,where p is the price per unit when q units are demanded.The point elasticity of demand when q = 100 is

A) -
B) -
C) -9.
D) -
E) -

Question 70

Determine the point elasticity η of the demand equation p = -
+ 30,where p > 0 and q > 0.

Question 71

Find the point elasticity of the demand equation p = 15 - 0.3q for the value q = 300,and determine whether demand is elastic,inelastic or has unit elasticity.

Question 72

Differentiate: g(x)=

Question 73

The demand function for a manufacturer's product is given by p = 300 -
,where p is the price per unit when q units are demanded.
(a)Determine the point elasticity of demand when q = 5.
(b)For q = 5,is demand elastic,inelastic,or does it have unit elasticity?
(c)For what value of q does demand have unit elasticity?

Question 74

The demand function for a manufacturer's product is given by p = 500 - 5q - where p is the price per unit when q units are demanded.The point elasticity of demand when q = 5 is

A) -0.5.
B) -1.
C) -1.5.
D) -4.
E) -6.

Question 75

Differentiate: f(x)=

Question 76

Determine the point elasticity of the demand equation: q =
- 10p + 200.

Question 77

Differentiate: f(x)= (10x - 4)∙

Question 78

Determine the point elasticity η of the demand equation p = -3q + 120,where p > 0 and q > 0.

Question 79

Differentiate: f(x)=

Question 80

Determine the point elasticity η of the demand equation pq = 81,where p > 0 and q > 0.