26. Consider the functions y = f(x) and y = g(x) whose graphs in red and blue, respectively, are shown in Figure 3.12. 4 -8 Figure 3.12 Functions y = f(x) (red) and y = g(x) (blue).
26. Consider the functions y = f(x) and y = g(x) whose graphs in red and blue, respectively, are shown in Figure 3.12. 4 -8 Figure 3.12 Functions y = f(x) (red) and y = g(x) (blue).
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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Question 26
![Level 1 DRILL PROBLEMS
1
22.
y
1
= 1
Use the chain rule to compute the derivative dy/dx for the
functions given in Problems 1 to 4.
1. у 3 и? + 1; и %— Зх — 2
23. (2х + 3у)? %3D 10
24. In(xy) = e²x
25. e*y + In y² = x
26. Consider the functions y = f(x) and y = g(x)
whose graphs in red and blue, respectively, are
shown in Figure 3.12.
+ 1; u =
-
2. у %3D 2и? —
и + 5; и — 1- х2
3. у %3
2iu = x² – 9
и — х2
-
4. у 3 и*; и 3D Inx
Differentiate each function in Problems 5 to 8 with respect
to the given variable of the function.
5. а. g(u) — и5
b. u(x) — Зх — 1
-
с. f(x) — (3х — 1)5
6. а. g(u) — из
b. u(x) — х2 + 1
c. f(x) = (x² + 1)³
7. а. g(u) — и15
b. u(x) — Зх2+ 5х — 7
4
-
-4
Figure 3.12 Functions y = f(x) (red) and y = g(x) (blue).
d
f[g(x)]],-2
d
a. Find
b. Find 8lf(x)],-2
|x=2
c. f(x) = (3x² + 5x – 7)15
8. a. g(u) = u?
b. u(х) — 5 —8х — 12х2
c. f(x) = (5 – 8x – 12x²)7
dx
|x=2
dx
27. The graphs of u = g(x) and y = f(u) are shown in
Figure 3.13.
-
-
"YA
Differentiate each function in Problems 9 to 18.
9. y = (5 – x +x*)°
10. у
10. y = e2+x²
-4
1
11. y =
12. y = e(x+1)7
(1+x – x)12
13. y = In x2
14. у
(2х + 12)"
4
6.
4
15. y = In(2x +5)
16. у —
= xe-x?
u = g(x)
y = f(u)
17. y = (x* – 1)1º(2x+ + 3)7
18. у —
4
x2
Figure 3.13 Chain rule with graphs.
Lijn
ligit diffc
ra Du ble
10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4db1e84-75df-498d-9686-5cabfd0e0c2f%2F17d855b3-3ff9-4537-a4d1-a37fc9f3fc62%2Fj9sedt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Level 1 DRILL PROBLEMS
1
22.
y
1
= 1
Use the chain rule to compute the derivative dy/dx for the
functions given in Problems 1 to 4.
1. у 3 и? + 1; и %— Зх — 2
23. (2х + 3у)? %3D 10
24. In(xy) = e²x
25. e*y + In y² = x
26. Consider the functions y = f(x) and y = g(x)
whose graphs in red and blue, respectively, are
shown in Figure 3.12.
+ 1; u =
-
2. у %3D 2и? —
и + 5; и — 1- х2
3. у %3
2iu = x² – 9
и — х2
-
4. у 3 и*; и 3D Inx
Differentiate each function in Problems 5 to 8 with respect
to the given variable of the function.
5. а. g(u) — и5
b. u(x) — Зх — 1
-
с. f(x) — (3х — 1)5
6. а. g(u) — из
b. u(x) — х2 + 1
c. f(x) = (x² + 1)³
7. а. g(u) — и15
b. u(x) — Зх2+ 5х — 7
4
-
-4
Figure 3.12 Functions y = f(x) (red) and y = g(x) (blue).
d
f[g(x)]],-2
d
a. Find
b. Find 8lf(x)],-2
|x=2
c. f(x) = (3x² + 5x – 7)15
8. a. g(u) = u?
b. u(х) — 5 —8х — 12х2
c. f(x) = (5 – 8x – 12x²)7
dx
|x=2
dx
27. The graphs of u = g(x) and y = f(u) are shown in
Figure 3.13.
-
-
"YA
Differentiate each function in Problems 9 to 18.
9. y = (5 – x +x*)°
10. у
10. y = e2+x²
-4
1
11. y =
12. y = e(x+1)7
(1+x – x)12
13. y = In x2
14. у
(2х + 12)"
4
6.
4
15. y = In(2x +5)
16. у —
= xe-x?
u = g(x)
y = f(u)
17. y = (x* – 1)1º(2x+ + 3)7
18. у —
4
x2
Figure 3.13 Chain rule with graphs.
Lijn
ligit diffc
ra Du ble
10
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