188 CHAPTER 3 Differentiation Rules 3.2 EXERCISES 1. Find the derivative of f(x) = (1 + 2x)(x - x) in two ways: by using the Product Rule and by performing the multiplica- tion first. Do your answers agree? x2 29. f(x) = 1 e 2. Find the derivative of the function 31-32 Find an equation the specified point. Vx x4-5x3 F(x) x2 1 + x + x2 31. y in two ways: by using the Quotient Rule and by simplifying first. Show that your answers are equivalent. Which method do 33-34 Find equation you prefer? given curve at the sp 33. y 2xex, (0, 3-26 Differentiate. - (x + 2x) e 4. g(x) 3. f(x)= (3x2 5x)e ex 35. (a) The curve 6. У 5. у - 1 - e Agnesi. F at the po (b) Illustrate ex x22 X 1 + 2x 8. G(x) 7. g(x) 2x+1 3- 4x line on t 9. H(u) (u - Vu) (u + u) 36. (a) The cur an equa 2) 10. J(v)= (v3 - 2v)(v (3, 0.3 (b) Illustr: line o -( 3 (y5y3) 1 11. F(y) = 37. (a) If f( (b) Chec 12. f(z) (1- e)(z + e?) com Vx 14. y 2 x x2 +1 38. (а) If f (b) Che 13. у — 3 1 1 со t3+3t 16. y 3 t 2t2-1 15. у б t2 4t3 39. (a) If (b) C b ae" 18. h(r) 17. y e(p +pvp) b e" 40. (a) L (b) 20. y (z2e)z + 19. y s2 4 + t VI 21. f(t)= 41. If f 22. V(t)= te' t - 3 42. If At xe 24. F(t)= 43. Su 23. f(x) Bt2 Ct3 11 x2 ex Fi (a х 26. f(x)= 1 25. f(x)= I1 Cx + d 44. S X + х 27-30 Find f'(x) and f"(x) Vxe 28. f(x) = 27. f(x) (x3 1)e 0 4HAC 0 03/110
188 CHAPTER 3 Differentiation Rules 3.2 EXERCISES 1. Find the derivative of f(x) = (1 + 2x)(x - x) in two ways: by using the Product Rule and by performing the multiplica- tion first. Do your answers agree? x2 29. f(x) = 1 e 2. Find the derivative of the function 31-32 Find an equation the specified point. Vx x4-5x3 F(x) x2 1 + x + x2 31. y in two ways: by using the Quotient Rule and by simplifying first. Show that your answers are equivalent. Which method do 33-34 Find equation you prefer? given curve at the sp 33. y 2xex, (0, 3-26 Differentiate. - (x + 2x) e 4. g(x) 3. f(x)= (3x2 5x)e ex 35. (a) The curve 6. У 5. у - 1 - e Agnesi. F at the po (b) Illustrate ex x22 X 1 + 2x 8. G(x) 7. g(x) 2x+1 3- 4x line on t 9. H(u) (u - Vu) (u + u) 36. (a) The cur an equa 2) 10. J(v)= (v3 - 2v)(v (3, 0.3 (b) Illustr: line o -( 3 (y5y3) 1 11. F(y) = 37. (a) If f( (b) Chec 12. f(z) (1- e)(z + e?) com Vx 14. y 2 x x2 +1 38. (а) If f (b) Che 13. у — 3 1 1 со t3+3t 16. y 3 t 2t2-1 15. у б t2 4t3 39. (a) If (b) C b ae" 18. h(r) 17. y e(p +pvp) b e" 40. (a) L (b) 20. y (z2e)z + 19. y s2 4 + t VI 21. f(t)= 41. If f 22. V(t)= te' t - 3 42. If At xe 24. F(t)= 43. Su 23. f(x) Bt2 Ct3 11 x2 ex Fi (a х 26. f(x)= 1 25. f(x)= I1 Cx + d 44. S X + х 27-30 Find f'(x) and f"(x) Vxe 28. f(x) = 27. f(x) (x3 1)e 0 4HAC 0 03/110
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...
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I need help with Calculus HW. I need to differentiate problem #25 on page 188, Section 3.2, of the James Stewart Calculus Eighth Edition textbook. I need help on simplifying the problem.
Transcribed Image Text:188
CHAPTER 3
Differentiation Rules
3.2 EXERCISES
1. Find the derivative of f(x) = (1 + 2x)(x - x) in two ways:
by using the Product Rule and by performing the multiplica-
tion first. Do your answers agree?
x2
29. f(x) =
1 e
2. Find the derivative of the function
31-32 Find an
equation
the specified point.
Vx
x4-5x3
F(x)
x2 1
+ x +
x2
31. y
in two ways: by using the Quotient Rule and by simplifying
first. Show that your answers are
equivalent. Which method do
33-34 Find equation
you prefer?
given curve at the sp
33. y 2xex, (0,
3-26 Differentiate.
- (x + 2x) e
4. g(x)
3. f(x)= (3x2 5x)e
ex
35. (a) The curve
6. У
5. у -
1 - e
Agnesi. F
at the po
(b) Illustrate
ex
x22
X
1 + 2x
8. G(x)
7. g(x)
2x+1
3- 4x
line on t
9. H(u) (u - Vu) (u + u)
36. (a) The cur
an equa
2)
10. J(v)= (v3 - 2v)(v
(3, 0.3
(b) Illustr:
line o
-(
3
(y5y3)
1
11. F(y) =
37. (a) If f(
(b) Chec
12. f(z) (1- e)(z + e?)
com
Vx
14. y 2 x
x2 +1
38. (а) If f
(b) Che
13. у —
3
1
1
со
t3+3t
16. y 3 t 2t2-1
15. у б
t2 4t3
39. (a) If
(b) C
b
ae"
18. h(r)
17. y e(p +pvp)
b e"
40. (a) L
(b)
20. y (z2e)z
+
19. y
s2
4 + t
VI
21. f(t)=
41. If f
22. V(t)=
te'
t - 3
42. If
At
xe
24. F(t)=
43. Su
23. f(x)
Bt2 Ct3
11
x2 ex
Fi
(a
х
26. f(x)=
1
25. f(x)=
I1
Cx + d
44. S
X +
х
27-30 Find f'(x) and f"(x)
Vxe
28. f(x) =
27. f(x) (x3 1)e
0
4HAC 0
03/110
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