Добавил:

Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.

Вуз:

Московский государственный университет путей сообщения

Предмет:

[НЕСОРТИРОВАННОЕ]

Файл:

proizv_i_graf

.pdf

Скачиваний:

Добавлен:

09.06.2015

Размер:

176.48 Кб

Скачать

☆

<<< < Предыдущая 12 / 42 3 4 > Следующая >>>

Задание • 9. Найти y′.

9.1.

x 3

y = arctg(

+ 1)

5 ln(x 1)

x + 2

9.2.

y = 2

x (x 3 x) arcsin 2 + px

x2 + 1

9.3. y =

arccos

2x 2

9.4. y =

ln(4x2

+ 1) + arcctg

+ 1

+ p

9.5. y = arcctg

9.6.y = 2x (2x + 1) arctg p

9.7. y = 85 arcsin 2x + 13 arctg px + px

9.8. y = x2 arccos

x3 + 1 + x3 + 1

9.9.

x2 + 1

y = arctg x2 1

2 ln

x + 1

9.10. y = arctg

(x + 2)p

arcctg

x 1

9.11. y =

+ 3x

1 +

x 1

√

(x + 1) arctg p

9.12. y =

9.13. y = arcsin p

x 2p

9.14. y = arcsin p

x 2p

9.15. y =

3x3

√

x + 1

arccos x

9.16. y = arcsin 3

9.17. y = arcsin x3 + 3 3 x

√

9.18. y = arcctg x arccos

x + 1

9.19.

y =

+ arccos

9.20.

x + 3p

y =

x + 1 2 arccos x

9.21. y =

(x + 2) arctg

x + 2

9.22.

y =

arcsin x x

x + 2

√

x2 + 1

x 7

9.23. y =

x + 1

7 arcsin

1 x

9.24. y =

arcctg x

1 + x

9.25. y = arccos

x 2

9.26. y =

arctg

x 1

√3

p3x

9.27. y = arcsin

1 + x 1

9.28. y =

arctg

3x + 1

9.29. y = arcctg

sin x cos x

y = arccos

tg x 1

9.30.

9.31. y = arcsin

x3 + 1

4 x2

9.32.

y =

x arccos x + 1 2 ln 2x

9.33. y =

arcctg √3

x + 1

9.34. y =

(1 x2) arctg p

2x + 3

1 + p

9.35. y = arcsin

1 p

x + 3

9.36. y =

arccos

Задание • 10. Найти y′.

10.1. y =

(ln sin 3x)x

10.19. y = logx+1 x2

10.20. y = log 2 (x + 1)

10.2. y = 2x

10.3. y = xex

10.21. y = (x3 + 1)x3

10.4. y = (x + 1)tg x

10.22. y = (1 + x2)x2

10.5. y = xecos x

10.23. y = (x sin x)x

10.6. y = (sin x)ln x

10.24. y = (x tg x) 2

10.7. y = xx3

10.25. y = (tg x)ex

10.8. y = 3x x2x

10.26. y = xarcsin x

10.9. y = logx 2x

10.27. y = xarctg x

10.10. y = logx(x2 + 1)

10.28. y = (ln x)arccos x

10.11. y = (tg px)e

10.29. y = (sin px)ln x

10.12. y = xetg x

10.30. y = (arctg x)arcsin x

10.13. y = 9x x9x

10.31. y = (arcctg x)x2+1

10.14. y = x2x ln x

10.32. y = (sin x)x ln x

10.15. y = (sin x)x2

10.33. y = (x2 + 1)sin p

10.16. y = (x + 1)sin x

10.34. y = (2x + e2)cos x

10.17. y = (1 x)sin x

10.35. y = (sin log2 x)cos x

10.18. y = (x

tg x

10.36. y = (arctg 3x)

+ 1)

Задание • 11. Найти y′.

11.1. y = ln 1 + 3x2 + 1 x

11.2. y = 47x2 + 1 arctg 9x

11.3. y = ln(e2x + e2x + 1)

11.4. y = arctg ln x

11.5. y = (x + 1)4 arccos 1 2x + 1

11.6. y = ln(3x + 9x2 + 1) p

11.7.y = ln 2 + x2 9x + 1 x + 2

11.8.			p
	y = arctg(5x)			5x 1
11.9. y =		x	+ log2	2x + 1
11.9. y =		x + 1	+ log2	x
		x + 1		x

11.10. y = arcsin e 3x

11.11. y = ln(e2x + ex 1)

11.12. y = x2 x arccos x 1

11.13. y = ln sin x + cos x arctg x

11.14. y = ln(5 + x + x + 5)

11.15. y = 3x2 + x 1 lg(3x2 1)

11.16. y = arccos ln x2

11.17. y = x 2 sin ex 2 x + 3

11.18. y = (x 1) 3 x 2 ln4 x

11.19.y = x3 1 arcctg 3 x

11.20. y = ln arctg x

11.21. y = e 3x arcsin e3x
11.22.					p
	y = 3x 2 ln(1 2 x)
		x3	7		1
11.23. y =			arccos		+ ln
11.23. y =			arccos	x	+ ln	x
	27			x		x

11.24.y = ln x2 + arctg x

		p		p
11.25.						2
11.25.	y = ln(1 +		x		x	2	9)
	y = ln(1 +		x		x		9)

15x

11.26.y = p arcctg p

11.27. y =

arccos

11.28. y =

arctg

11.29. y = log2 e2x + ln 2x

11.30. y = ex2 arcsin x2

11.31. y = arctg log2 sin x

11.32.

y = log3 arcsin

1 x

11.33. y =

+ log4

1 x

x2 3

x2 + 1

11.34. y =

sin ln x2

11.35. y = e1 x

x + 1

arctg

11.36. y =

e2x

arcctg log5

Задание • 12. Найти y′.

12.1. y = x arcsin √

px + 2

12.2.

x + 2

y =

arccos

x + 1

12.3. y =

10x (10

x2)

12.4. y = x2 sin x2 + x2

1		1
12.5. y =		+ tg
	x2		x2

12.6. y = 2p1 x2 + exp1 x2 p

12.7.y = x arcsin x

√1

12.8.y = (x + 3)(x 2) + e2x

12.9. y = x ln( 1 x + 1 + x)

12.10.y = 12(arccos x x2)7x

12.11.y = arcsin p 3

x 3

√

12.12.y = ln 5 x 2 + 5x x 1 )(


	1		1
12.13. y =						arcctg x
	2				x2 1
12.14. y =		p		ln x

				x3 + 1

12.15.y = ln( x + 1 + 2)e x+1

12.16.

y =

+ 12x 16 arctg

12.17. y =

x3 x + 1

(x + 1)3

12.18. y =

arcctg

2x2 + 1

ln p

12.19. y =

x2 1

px2 + 1 + 1

12.20. y = 3 ln(

3 + x +

x 3)

2x + 1

12.21. y = arcsin

12.22. y = x3 arctg x3

+ px3 + 1

12.23. y = 3 ln

1 p

x2 + 4

x arctg x

12.24. y =

x2 + x

+ 2 ln p

12.25. y =

(x + 1)(2

x + 1

√

y = ln(x + p

) +

1 + x

1 + x2

12.26.		3x
		3x
12.27. y = 2x+1 ln(x + 1)
12.28. y = arctg2 x p
12.28. y = arctg2 x p	arccos x

12.29.y = x ln 5 x

p p

12.30. y = arcsin 3 x 3 arcsin x

12.31.y = e 1 x arctg 3 x2 + 1

12.32. y = x2 + 1 lg3 arcsin x

12.33. y = 2x ln

1 + p

x2 3

12.34. y =

log 1

arctg px

12.35. y = arcsin

pln x

12.36. y = px + 1 5 ln2 px + 2

Задание • 13. Найти производную yx′ .

x(t) = ln p

13.1.

1 t2

y(t) = t arcsin t

13.2.

x(t) = e

sin t

y(t) = t

tg t

13.3.

x(t) = p

t t

√

y(t) = arctg

1 t

13.4.

x(t) = p

y(t) = p

arcsin p

1 t

13.5.

x(t) =

t2 ,

t2 ln t

y(t) =

ln p1

13.6.

x(t) = arctg(t + 1),

y(t) = arcsin p1 t

x(t) = ln p

sin t,

13.7.

y(t) = ln cos t

x t

sin t,

13.8.

(

) = ln 1

y(t) =

cos2 t

13.9.

x(t) = t t + 1,

y(t) = ln(1 + p

t + 1)

x(t) = arctg t,

13.10.

y(t) = ln pt

x(t) = arccos p

t + 1

13.11.

y(t) = ln(t + 1)

x(t) = arccos t,

13.12.y(t) = √1 + pt

x(t) = arcsin2 t,

13.13.y(t) = tp1 t

x(t) = ln 1t ,

y(t) = arcsin(1 t2)

x(t) = t2 + 1,

y(t) = p 1

1 t2

x(t) = arctg et,

y(t) = et + 2

x(t) = ln sin t, y(t) = ctg t

x(t) = tg(2e2 ), y(t) = ln tg et

x(t) = 2t + t3, y(t) = arctg t

x(t) = lg(t + t2 + 1),

√ p y(t) = t t2 + 2

x(t) = arctg(tg t), y(t) = arcsin(cos t)

x(t) = t2 + t + 1, y(t) = sin(t2 + 1)

x(t) = sin t + cos t,

y(t) = arcsin t + arccos t

x(t) = sin ln t, y(t) = ln sin t

x(t) = t3 + 1, y(t) = sin3 t + 1

x(t) = lg(t2 + t + 1),

p y(t) = sin(1 + t)

x(t) = 1 , ln t 1 y(t) = ln t

x(t) = arcsin 1, t 1 y(t) = arccos t

x(t) = 1 + cos2 t, y(t) = cos t

x(t) = arcsin(1 + t2), y(t) = arccos2 t

x(t) = t + t2 + 1,

y(t) = ln(t + t2 + 1)

x(t) = t3 + 2t2 1,

p y(t) = arcctg(t sin t)

x(t) = ctg(t + ln t), y(t) = tg(1 + et)

x(t) = t2 + cos(t2 1), y(t) = t sin t2

x(t) = arctg(2t + 3t), y(t) = lg(t3 4)

x(t) = arcctg(lg t ln t), y(t) = t2 2t

Задание • 14. Найти производную второго порядка от функции, заданной параметрически.

x(t) = 2t cos t,

14.1.y(t) = 3 + sin t

x(t) = ln(t 1),

14.2.y(t) = pt2 + 1

x(t) = sin3 t,

14.3.y(t) = ctg2 t

x(t) = 2et,

14.4.y(t) = arccos t

x(t) = t3,

14.5.	y(t) =		1

		t3	+ 4

x(t) = tg2 t,

14.6.y(t) = cos t

14.7.	3
	x(t) = pch t,
	y(t) = sh t

x(t) = ln(3 cos t),

14.8. y(t) = 2 sin t

14.9.		(	) =		1
	x t			ctg t,
					p
y(t) =				cos 2t
14.10.
14.10.						2t
					p
		x(t) =			3	t 1,
	y(t) =				3

					1 t 1
	x(t) =					,
14.11.	x(t) =				t2	,
					3	1
	y(t) =					1

					t	+ 1

x(t) = 3et,

14.12.y(t) = arctg t

x(t) = 2(1 + sin t), y(t) = 4(t 2 cos t)

x(t) = arcsin t,

y(t) = t3

3 x(t) = sin t, y(t) = cos3 t

x(t) = 3t cos t, y(t) = 3 sin t

x(t) = et(cos t + sin t), y(t) = et(sin t cos t)

x(t) = sin 2t, y(t) = 4 cos3 t

x(t) = t4 ,

4 t y(t) = ln 2

x(t) = sh t, y(t) = th t

x(t) = 4 t, y(t) = ln(t + 5)

x(t) = et,

y(t) = arccos 2t

x(t) = 2t , t + 1 p

y(t) = t

x(t) = 4 t + 1, y(t) = 1t

x(t) = t cos t sin t, y(t) = t sin t + cos t

x(t) = sin 3t,

y(t) = 2(cos 2t + sin t)

x(t) = 3 1 t, y(t) = 1t

x(t) = sh2 t,

p y(t) = ch t

x(t) = ln tg t, y(t) = sin t

x(t) = ln ctg t, y(t) = cos t

x(t) = lg(2t 1),

14.31.y(t) = sh 2t

x(t) = arcsin 4t,

14.32.y(t) = 1

		1
		x(t) = p		,
14.33.			t
		3			+ 1
	y(t) = pt2				+ 1

x(t) = ch3 t,

14.34. p y(t) = 3 th t

4t 1,

14.35.y(t) = lg t

tx(t) =

x(t) = cos lg 2t,

14.36.y(t) = tg 3t

15.32. y = sin(x + 1) +

Задание • 15. Найти производную

15.1. y = cos(3x 1) sin 2x

15.2. y = (x + 4)5

15.3. y = ln(2x + 3)

15.4. y = 23x+1 p

15.5.y = 34x 1

15.6.y = sin(5x + 3) + 4 cos(1 x)

15.7. y = x 2

15.8. y = 43x 1

15.9. y = lg(4 x)

15.10. y = x + 3 x 2

15.11. y = log2(2x 1)

15.12. y = sin x cos x

4 + x

15.13. y = 3(x + 1)

15.14. y = 4 sin kx + 2 cos mx

15.15. y = akx+3

15.16. y = 3 2 3x

15.17. y =

ax + b

15.18. y =

3x + 5

9x + 12

n-го порядка.

15.19. y = (ax2 + bx + c)5 p

15.20.y = 12 51 x

15.21.y = log4(12x + 13)

15.22.y = 143x

15.23. y = (21 x)3

15.24. y = 54 x

15.25. y = 2x 1 x + 2

15.26. y = sin x + e2x

15.27. y = 5 cos x + ex

15.28. y = log2(17x 2)

15.29. y = 3 2x

15.30. y = log11(4x + 3)

15.31. y = ln(x + 1) + ex

15.33. y = cos(2x 1) + e2x 1

15.34. y = 7 54x 3

15.35. y = x 4

15.36. y = log3(4x 5)2

Задание • 16. Найти производную неявной функции.

16.1.xy2 x2y = 0

16.2.sin(xy) xy = 0

16.3.cos(1 x3y3) = 0

16.4.tg x + y = 2 x y

16.5.sin x(y 3) + cos(xy) = 1

16.6.	x y3 + sin(xy)	= 3
	x2y2 + 4x

16.7.exy xy2 = 4

16.8.x3y2 2xy2 + xy = 0

16.9.y tg x sin2(xy) = 0

16.10.x3 y3 + 3x2y = 0

16.11.y3 x3 3xy2 = 0

16.12.x2 sin(x y)2 = 1

16.13.tg(x2y) ctg(xy2) = 2

16.14.ln(xy x2y3 + 1) = 4

16.15.arctg x + y = 1 x y

16.16. arcsin		x2y		2x3y3 = 1
	(x y)2
16.17. arccos		1 + xy	xy = 2
		exy

16.18. arctg(xy2 x2y) 3xy3 = 0

ex y

16.19. arcsin x y 2y2 = 0 p

x y

16.20. arctg 1 py y = 0

ex 3y

16.21. x y = 1

16.22. ln y + 6x 1 = 0 y

16.23. e 2 cos y cos(xy) = 0

√

16.24. 3 sin(xy2) cos(x2y) = 1

16.25.ln(cos x cos y) = 2

√

16.26.5 tg(x y) + ctg(x + y) = 1

16.27.epy sin(x y) x2y = 1

16.28.ln(pxy + x3y3) 2xy = 0

16.29.(x + y)(x y)(x2 y2) = 1

√

16.30. sin(x2 y2) + 3 x3 y3 = 0

16.31. y sin(xy + x) + 2y tg(x + y) = 3x

16.32. xy2 x3y + 2xy = x2 tg(x2y)

16.33.ln(x + y) sin(x 2y) = xy

16.34.tg(x2 + y2 1) = ln(x + y 1)

16.35.exy+sin(xy) = x y

√

16.36.sin x + tg(x2 + y2) = y

Раздел 2. ГРАФИКИ ФУНКЦИЙ

Задание • 1. Построить графики функций, используя при их исследовании первую производную.

<<< < Предыдущая 12 / 42 3 4 > Следующая >>>

Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]

#
28.03.201643.01 Кб41Prakticheskoe_zanyatie_1.doc
#
28.03.2016160.82 Кб179Pravila_tekhnicheskoy_expluatatsii_PTE.docx
#
09.06.2015357.28 Кб22Primer.docx
#
28.03.20162.32 Mб4Primer_BP.docx
#
28.03.2016194.12 Кб16profstandartspecialist_po_upravleniyu_personalom.docx
#
09.06.2015176.48 Кб7proizv_i_graf.pdf
#
09.06.2015669.7 Кб24Prom_transport_metodichka.doc
#
09.06.2015647.46 Кб11protection_24.pdf
#
09.06.2015911.36 Кб16pr_mt_286_21122010_pril-1.doc
#
08.06.2015764.42 Кб23pte-2012.doc
#
09.06.20151.12 Mб23public_administration.doc