11. f(t)=t Int -t 12. y = x² Inx 14. y = (ax+ b)' In (ax +b) 16. f(w) = log (w² + 2w + 1) 18. y =x² log,x 43. У 13. y =x' In (2r + 5) 45. F 15. y= log; (8r 1) 17. y =x² + log, (x +4) when In z 19. f(z) = x2 20. у 46. F %3D In x + 21. у %3 + 3x +x 22. y = In x100 at the In x 23. y = In (x² + 4x + 5)3 24 - 6 In 3/ 47
11. f(t)=t Int -t 12. y = x² Inx 14. y = (ax+ b)' In (ax +b) 16. f(w) = log (w² + 2w + 1) 18. y =x² log,x 43. У 13. y =x' In (2r + 5) 45. F 15. y= log; (8r 1) 17. y =x² + log, (x +4) when In z 19. f(z) = x2 20. у 46. F %3D In x + 21. у %3 + 3x +x 22. y = In x100 at the In x 23. y = In (x² + 4x + 5)3 24 - 6 In 3/ 47
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
15 and 39
![31. y = In [(ax² + bx + cP(hx² + kx + l)ª]
If y = log 1), find the of of y with to x.
Ch Addmonal D
AMPLE S
Differentissey= kogy.
so. Marginal C
Following the foregoing procedire, we have
(xu)-
(In 2)x
51. Supply
price of p de
Because
301
Find the ra
52. Soun
decibels,
301
log; More generally,
we can express
(n 9301)-
xp
(In 2)r
as
np 9301
levels / a
APPLY IT
threshol
EXAMPLE 6
2. The intensity of an earthquake is mea-
sured on the Richter scale. The reading
the louc
is given by R = log
intensity and lo is a standard minimum
where 1 is the
intensity. If lo = 1, find
dR
the rate of
In 10
To de
change of the Richter-scale reading with
respect to the intensity.
xp
xp
IP
use
(2)
In 10(2x + 1)
Dung
In 10 2x + 1
PROBLEMS 12.1
In Problems 1–44, differentiate the functions. If possible, first use
properties of logarithms to simplify the given function.
31. y= In [(ax² + bx + cP(hx² + kx + 1)9]
32. v= In [(5x + 2)*(8x – 3)°] 33. y = 13 In (x² V5x
1. y=alnx
rul
4. y= In (5x – 6)
6. y= In (5x + 3x² + 2x + 1) 7. y= In (1 – x²)
8. y= In (-x² + 6x)
10. f(r) = In (2r4 - 3r2 + 2r + 1)
11. f(t) =t Int-t
13. y =x In (2r + 5)
3. y = In (3x – 7)
%3D
6.
5. y = In x?
34. y = 6 In
36. y = (ax? + bx + c) In (h² + kx + 1)
||
37. y = In x + In³ x
39. y = In (ax)
41. y = In /f(x)
43. y = V4+3 In x
45. Find an equation of the tangent line to the curve
38. y = x'n 2
40. y = In² (2x + 11)
42. y = In (x' /2x+1)
9. ƒ(X)= In (4X 6 + 2X ³)
12. y = x² Inx
%3D
%3D
15. y= log, (8x – 1)
17. y =x² + log, (r2 + 4)
14. y = (ax + b)³ In (ax + b)
16. f(w) = log (w² + 2w + 1)
18. y = x² log,x
%3D
y = In (x² – 3x - 3)
(*++x) u =
when x = 4.
= (2)f '61
20. y=
21. y=
46. Find an equation of the tangent line to the curve
23. y = In (x² + 4x +5)³
22. y = In r00
y = x In x-x
%3D
at the point where x = 1.
%3D
24. y = 6 In r
zX+ I^ u[6 = &
26. f(t) = In
47. Find the slope of the curve y =
when x = 3.
27. f(1) = In
48. Marginal Revenue
the demand function is p = 25/ In (q+2).
Find the marginal-revenue function if
2x+ 3
+ 19 +1
28. y = In
%3D
1+x²
3x – 4
3Dd
29. y = In
49. Marginal Cost
A total-cost function is given by
30. y = In
c = 25 In (q + 1)+ 12
Find the marginal cost when q = 6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e2d6f28-e3d7-414c-b1d4-a752131175c2%2F5d3ad02c-9dd4-4e59-af5b-355176ca08f0%2F3zqdy4d.jpeg&w=3840&q=75)
Transcribed Image Text:31. y = In [(ax² + bx + cP(hx² + kx + l)ª]
If y = log 1), find the of of y with to x.
Ch Addmonal D
AMPLE S
Differentissey= kogy.
so. Marginal C
Following the foregoing procedire, we have
(xu)-
(In 2)x
51. Supply
price of p de
Because
301
Find the ra
52. Soun
decibels,
301
log; More generally,
we can express
(n 9301)-
xp
(In 2)r
as
np 9301
levels / a
APPLY IT
threshol
EXAMPLE 6
2. The intensity of an earthquake is mea-
sured on the Richter scale. The reading
the louc
is given by R = log
intensity and lo is a standard minimum
where 1 is the
intensity. If lo = 1, find
dR
the rate of
In 10
To de
change of the Richter-scale reading with
respect to the intensity.
xp
xp
IP
use
(2)
In 10(2x + 1)
Dung
In 10 2x + 1
PROBLEMS 12.1
In Problems 1–44, differentiate the functions. If possible, first use
properties of logarithms to simplify the given function.
31. y= In [(ax² + bx + cP(hx² + kx + 1)9]
32. v= In [(5x + 2)*(8x – 3)°] 33. y = 13 In (x² V5x
1. y=alnx
rul
4. y= In (5x – 6)
6. y= In (5x + 3x² + 2x + 1) 7. y= In (1 – x²)
8. y= In (-x² + 6x)
10. f(r) = In (2r4 - 3r2 + 2r + 1)
11. f(t) =t Int-t
13. y =x In (2r + 5)
3. y = In (3x – 7)
%3D
6.
5. y = In x?
34. y = 6 In
36. y = (ax? + bx + c) In (h² + kx + 1)
||
37. y = In x + In³ x
39. y = In (ax)
41. y = In /f(x)
43. y = V4+3 In x
45. Find an equation of the tangent line to the curve
38. y = x'n 2
40. y = In² (2x + 11)
42. y = In (x' /2x+1)
9. ƒ(X)= In (4X 6 + 2X ³)
12. y = x² Inx
%3D
%3D
15. y= log, (8x – 1)
17. y =x² + log, (r2 + 4)
14. y = (ax + b)³ In (ax + b)
16. f(w) = log (w² + 2w + 1)
18. y = x² log,x
%3D
y = In (x² – 3x - 3)
(*++x) u =
when x = 4.
= (2)f '61
20. y=
21. y=
46. Find an equation of the tangent line to the curve
23. y = In (x² + 4x +5)³
22. y = In r00
y = x In x-x
%3D
at the point where x = 1.
%3D
24. y = 6 In r
zX+ I^ u[6 = &
26. f(t) = In
47. Find the slope of the curve y =
when x = 3.
27. f(1) = In
48. Marginal Revenue
the demand function is p = 25/ In (q+2).
Find the marginal-revenue function if
2x+ 3
+ 19 +1
28. y = In
%3D
1+x²
3x – 4
3Dd
29. y = In
49. Marginal Cost
A total-cost function is given by
30. y = In
c = 25 In (q + 1)+ 12
Find the marginal cost when q = 6.
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