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In exercises 1–24, differentiate each function. D f(x) = x*e* (2. F(x)= e2* cos 4.x 3. f(t) =t +2' 4. )f (t) = t43t

In exercises 1–24, differentiate each function. D f(x) = x*e* (2. F(x)= e2* cos 4.x 3. f(t) =t +2' 4. )f (t) = t43t

Calculus: Early Transcendentals
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 the answers for the circled quistions please 

6:29 AM Thu 14 Oct 36% < 88 mat113_Chapter2 - ... 00 x mat113_Chapt... O x Untitled (6) Untitled (7) X PHY103Lab_Simpl... X PHY103-ForceTabl... In exercises 1–24, differentiate each function. om D f(x) = x²e* 2. F(x) = e2* cos 4.x an- ain 3. f(t) =t +2' (4. )f (t) = 14 ph 5. f(x)= 2e4x+1 6. f(x) = (1/e)* ng 7. h(x) = (1/3)*² 8. )h(x) = 4-x² an 9. f(u) — еu?+4и 10. f(u) = 3etan u rer. e4w 11. ƒ(w) = ent W 12, f(w) = e6w cal 13. f(x) — In 2х 14. f(x) = In /8x nd 15.) f (t) = ln (t³ + 3t) 16. (t) = t° In t %3D ge 17. g(x) = In (cos x) 18. g(x) = cos x In(x2 + 1) ns. to 19. (a) f (x) = sin (In x?) (b) g(t) = In (sint²) VIn x (20. (a) f(x) In Vi 1/4 (b) g(t) = t are 21. (a) h(x)= e* In x (b) f(x) = elnx pes et 22. (а) h(х) — 2° (b) f (x) = 2x
Transcribed Image Text:6:29 AM Thu 14 Oct 36% < 88 mat113_Chapter2 - ... 00 x mat113_Chapt... O x Untitled (6) Untitled (7) X PHY103Lab_Simpl... X PHY103-ForceTabl... In exercises 1–24, differentiate each function. om D f(x) = x²e* 2. F(x) = e2* cos 4.x an- ain 3. f(t) =t +2' (4. )f (t) = 14 ph 5. f(x)= 2e4x+1 6. f(x) = (1/e)* ng 7. h(x) = (1/3)*² 8. )h(x) = 4-x² an 9. f(u) — еu?+4и 10. f(u) = 3etan u rer. e4w 11. ƒ(w) = ent W 12, f(w) = e6w cal 13. f(x) — In 2х 14. f(x) = In /8x nd 15.) f (t) = ln (t³ + 3t) 16. (t) = t° In t %3D ge 17. g(x) = In (cos x) 18. g(x) = cos x In(x2 + 1) ns. to 19. (a) f (x) = sin (In x?) (b) g(t) = In (sint²) VIn x (20. (a) f(x) In Vi 1/4 (b) g(t) = t are 21. (a) h(x)= e* In x (b) f(x) = elnx pes et 22. (а) h(х) — 2° (b) f (x) = 2x
6:29 AM Thu 14 Oct 36% mat113_Chapter2 - ... 00 x mat113_Chapt... O x Untitled (6) Untitled (7) X PHY103Lab_Simpl... X PHY103-ForceTabl... 182 CHAPTER 2 Differentiation 23, (a) ƒ (x) = In (sin x) (b) f(t) = = In (sec t + tan t) 24. (a) f (x) = e2*x³ (b) f(w) = Ve2w + w³ •.• • In exercises 25–28, find an equation of the tangent line to y = f(x) at x = 1. 25. f(x) = 3er? 26. f(x) = Zre E 27. f(x)= x² In x 28. f(x) = 2 In x3 In exercises 29 and 30, find all values of x for which the tangent line to y = f (x) is horizontal. 29. la) -2r f (x) = xe (b) f(x) = xe-3x 30. (а) f (x) — х?е-2х (b) f(x) = x²e-3x ... .. In exercises 31–34, the value of an investment at time t is given by v(t). Find the instantaneous percentage rate of change. 31. v(t) = 100 3' 32. v(t) = 100 4' 33. v(t) = 40 e0.41 34. v(t) = 60 е -0.2г •..
Transcribed Image Text:6:29 AM Thu 14 Oct 36% mat113_Chapter2 - ... 00 x mat113_Chapt... O x Untitled (6) Untitled (7) X PHY103Lab_Simpl... X PHY103-ForceTabl... 182 CHAPTER 2 Differentiation 23, (a) ƒ (x) = In (sin x) (b) f(t) = = In (sec t + tan t) 24. (a) f (x) = e2*x³ (b) f(w) = Ve2w + w³ •.• • In exercises 25–28, find an equation of the tangent line to y = f(x) at x = 1. 25. f(x) = 3er? 26. f(x) = Zre E 27. f(x)= x² In x 28. f(x) = 2 In x3 In exercises 29 and 30, find all values of x for which the tangent line to y = f (x) is horizontal. 29. la) -2r f (x) = xe (b) f(x) = xe-3x 30. (а) f (x) — х?е-2х (b) f(x) = x²e-3x ... .. In exercises 31–34, the value of an investment at time t is given by v(t). Find the instantaneous percentage rate of change. 31. v(t) = 100 3' 32. v(t) = 100 4' 33. v(t) = 40 e0.41 34. v(t) = 60 е -0.2г •..
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