G(x)=уg(fx)) 00 o )7-26 Find f'(x).51-54 Fi7. f(x) = (x+ 2x)3728. f(x) = (3x + 2x- 1)51. y x-(-2)--279. f(x) =1pl10. f(x)x5x+ 1)3x53. у 3X411. f(x) =12. f(x)= Vx3- 2x+5(32-2x+ 1)355-58 Fi13. f(x)= V4+ V3x14. f(x)= /12+ Vx355. y covioi15. f(x) sin16. f(x) = tan Vx56. А 317. f(x) = 4 cos5X418. f(x) = 4x 5 sin20. f(x) tan (x3)19. f(x)= cos2 (3Vx)4= COSd57.[adwwOd ebutitg21. f(x) 2 sec2 (x7)X322. f(x) = cos=COSx + 158. x= C23. f(x) = Vcos (5x)24. f(x) V3x sin (4x)259. (а) U3-325. f(x)= [x+ csc (x+3)]ue Isino6 9nolstic- sec (4x2-2)12126. f(x) [x-4(b) Udegr27-40 Find dy/dx.(c) Fi327. y x sin (5x)328. y Vx tan' (x)inX(d) Fisin x530. y29. y xsec (1/x)atsec (3x+ 1)32. y sin (tan 3x)31. y cos (cos x)60. (a) Ustio1 + csc (x2)Cot (x)334. y33. y cos' (sin 2x)(b) Usgra35. y (5x + 8)' (1 - Vx)36. y= (x2 +x) sin x(c) Firusi1731 +x1 -x22Xx- 538. y37. у %3the2x+ 1(d) Fin(2x+3)339. y (4x2- 1)840. y[1sin3 (x)112theCoto

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Asked Sep 19, 2019
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#15. Find the derivative

 

f(x) = sin(1/x2)

G(x)=
у
g(fx)) 00 o )
7-26 Find f'(x).
51-54 Fi
7. f(x) = (x+ 2x)
37
2
8. f(x) = (3x + 2x- 1)
51. y x
-(-2)
--2
7
9. f(x) =
1pl
10. f(x)x5x+ 1)
3
x
53. у 3
X
4
11. f(x) =
12. f(x)= Vx3- 2x+5
(32-2x+ 1)3
55-58 Fi
13. f(x)= V4+ V3x
14. f(x)= /12+ Vx
3
55. y c
ovio
i
15. f(x) sin
16. f(x) = tan Vx
56. А 3
17. f(x) = 4 cos
5
X
4
18. f(x) = 4x 5 sin
20. f(x) tan (x3)
19. f(x)= cos2 (3Vx)
4
= COS
d
57.
[a
dw
wOd ebutitg
21. f(x) 2 sec2 (x7)
X
3
22. f(x) = cos
=COS
x + 1
58. x= C
23. f(x) = Vcos (5x)
24. f(x) V3x sin (4x)
2
59. (а) U
3
-3
25. f(x)= [x+ csc (x+3)]
ue Isino
6 9nols
tic
- sec (4x2-2)1
21
26. f(x) [x
-4
(b) U
de
gr
27-40 Find dy/dx.
(c) Fi
3
27. y x sin (5x)
3
28. y Vx tan' (x)
in
X
(d) Fi
sin x
5
30. y
29. y xsec (1/x)
at
sec (3x+ 1)
32. y sin (tan 3x)
31. y cos (cos x)
60. (a) Us
tio
1 + csc (x2)
Cot (x)
3
34. y
33. y cos' (sin 2x)
(b) Us
gra
35. y (5x + 8)' (1 - Vx)
36. y= (x2 +x) sin x
(c) Fir
usi
17
3
1 +x
1 -x2
2
X
x- 5
38. y
37. у %3
the
2x+ 1
(d) Fin
(2x+3)3
39. y (4x2- 1)8
40. y
[1sin3 (x)112
the
Coto
help_outline

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G(x)= у g(fx)) 00 o ) 7-26 Find f'(x). 51-54 Fi 7. f(x) = (x+ 2x) 37 2 8. f(x) = (3x + 2x- 1) 51. y x -(-2) --2 7 9. f(x) = 1pl 10. f(x)x5x+ 1) 3 x 53. у 3 X 4 11. f(x) = 12. f(x)= Vx3- 2x+5 (32-2x+ 1)3 55-58 Fi 13. f(x)= V4+ V3x 14. f(x)= /12+ Vx 3 55. y c ovio i 15. f(x) sin 16. f(x) = tan Vx 56. А 3 17. f(x) = 4 cos 5 X 4 18. f(x) = 4x 5 sin 20. f(x) tan (x3) 19. f(x)= cos2 (3Vx) 4 = COS d 57. [a dw wOd ebutitg 21. f(x) 2 sec2 (x7) X 3 22. f(x) = cos =COS x + 1 58. x= C 23. f(x) = Vcos (5x) 24. f(x) V3x sin (4x) 2 59. (а) U 3 -3 25. f(x)= [x+ csc (x+3)] ue Isino 6 9nols tic - sec (4x2-2)1 21 26. f(x) [x -4 (b) U de gr 27-40 Find dy/dx. (c) Fi 3 27. y x sin (5x) 3 28. y Vx tan' (x) in X (d) Fi sin x 5 30. y 29. y xsec (1/x) at sec (3x+ 1) 32. y sin (tan 3x) 31. y cos (cos x) 60. (a) Us tio 1 + csc (x2) Cot (x) 3 34. y 33. y cos' (sin 2x) (b) Us gra 35. y (5x + 8)' (1 - Vx) 36. y= (x2 +x) sin x (c) Fir usi 17 3 1 +x 1 -x2 2 X x- 5 38. y 37. у %3 the 2x+ 1 (d) Fin (2x+3)3 39. y (4x2- 1)8 40. y [1sin3 (x)112 the Coto

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Expert Answer

Step 1

Find the dy/dx.

1
f(x) sin
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1 f(x) sin

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Step 2

Here given function is composition of f(g(x)) of two functions:

f(u) sinu
1
ug(x)
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f(u) sinu 1 ug(x)

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Step 3

Now applying chain r...

d
(f(g(x)) u)* (g(x)'
du
(f(g(x))"=
1
-(sin(u))
dux'
sin
du
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d (f(g(x)) u)* (g(x)' du (f(g(x))"= 1 -(sin(u)) dux' sin du

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Tagged in

Math

Calculus

Derivative