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матем2 1-модуль

Total questions: 77

Worksheet time: 39mins

Name

Class

Date

U = 2x³ + 30xy + 100x + 12 y , d²u / dydx = ?

-6

30y

-30y

100y

U = ln ( 2xsiny ), d²u / dydx = ?

-2

-1

U = 2x³+ 30xy + 100x +12y , d²u / dy²

-3

-1

U = 2x³ + 30xy + 100x + 12y , d²u / dx²

12x

30y

-12y

3x-100

U = x²y , d²u / dydx = ?

-2y

-3y

U = ln ( x² + y³ ) , du / dy = ?

3y² / x² + y³

3y³ / x² + y³

-3y² / x² + y³

2y² / x³ + y²

4y² / x³ + y²

U = ln ( x⁴ + y³ ) , du / dx = ?

4x³ / x⁴ + y³

6x³ / x⁴ - y³

2y³ / x⁴ + y³

5x³ / x³- y⁴

4y³ / x³ + y⁴

U = e^2x+3y , du / dx = ?

2e ^{2x + 3y}

3e ^2x+3y

-2e ^2x+3y

xe ^2x+3y

-ye ^2x+3y

U = e^2x+3y , du / dy = ?

3e ^2x+3y

-2e^2x+3y

2e ^2x+3y

ye^2x+3y

-xe ^2x+3y

10.

U = e^2x+3y , du / dydx = ?

6e^2x+3y

-5e ^2x+3y

7xe ^2x+3y

2e ^2x+3y

-3ye ^2x+3y

11.

U = cos ( 3x - 5y ) , du / dx = ?

-3sin ( 3x - 5y )

-5cos ( 3x - 5y )

4xsin ( 3x - 5y )

-3ycos ( 3x - 5y )

2sin ( 3x - 5y )

12.

U = cos ( 3x - 5y ) , du / dy = ?

5sin ( 3x -5y )

5ycos ( 3x - 5y )

4sin ( 3x - 5y )

4xcos ( 3x - 5y )

-5xsin ( 3x - 5y )

13.

U = ln ( 2xsiny ) , du / dx = ?

1 / x

1 / y

1 / sinx

1 / siny

1 / cosx

14.

U = sinx × tgy , du / dx = ?

cosxtgy

sinxctgy

cosxctgy

sinx + tgy

cosx - tgy

15.

U = lncos ( 2x + y ) , du / dx = ?

-2sin ( 2x + y ) / cos ( 2x + y )

2ysin ( 2x + y ) / cos ( 2x + y )

-2cos ( 2x + y ) / sin ( 2x + y )

2tg ( 2x + y ) / cos ( 2x + y )

-2ctg ( 2x + y ) / sin ( 2x + y )

16.

Z = f ( x , y ) , dz = ?

df × dx / dx + df × dy / dy

df × dx / dy + df × dy / dx

df × dx / dx - df × dy / dy

df × dx / dy - df × dy / dx

df × dy / dy - df × dx / dx

17.

xdx + ydy = 0 , y ( x ) = ?

√ 2C - x²

Cx²

x² + C

√ x + C

C / x

18.

dy - dx = 0 , y ( x ) = ?

x + C

x² / 2 + C

Cx²

x² + C

19.

dy - x³dx = 0 , y ( x ) = ?

x⁴ / 4 + C

x³ / 3 + C

x² / 2 + C

x⁵ / 5 + C

-x⁴ / 4 + C

20.

dy - x³dx = 0 , y ( x ) = ?

x⁴ / 4 + C

x³ / 3 + C

x² / 2 + C

x⁵ / 5 + C

-x⁴ / 4 + C

21.

U = e^2x+3y , d²u / dy² = ?

9e^2x+3y

6e^2x+3y

3e^2x+3y

2e^2x+3y

4e^2x+3y

22.

U = ln ( 2xsiny ) , du / dy = ?

ctgy

tgy

2ctgy

2tgy

lny / cosx

23.

dy - dx = 0 , y ( 0 ) = 1 , y ( x ) = ?

x+1

-x

x-2

2 / x

24.

dx - 2dy = 0 , y ( x ) = ?

x / 2 + C

x - 2C

2x + C

2 / x - C

x² / C

25.

5dx + dy = 0 , y ( x ) = ?

-5x + C

x² / 5 + C

x / 5 + C

5x² / 2 + C

5C + x

26.

U = lncos ( 2x+y ) , du / dy = ?

-tg ( 2x+y )

2tg ( 2x+y )

-ctg ( 2x+y )

tg ( 2x+y ) / cos ( 2x+y )

-ctg ( 2x+y ) / -cos (2x+y )

27.

dy + 5dx = 0 , y ( 0 ) = 0 , y ( x ) = ?

-5x

5+x

x-5

5 / x

28.

U = sinx × tgy , du / dy = ?

sinx(1+tg²y)

sinx(1-ctg²y)

cosx(1+3tg²y)

cosx(1-ctg²y)

sin(1+2ctg²y)

29.

z = arctg √x / y , du / dy = ?

1 / 2(x+y) √x / y

4 / 5(x-y) √y / x

-3 / 4(x+y) √x / y

2 / 3(x-y) √y / x

1 / (x+y) √y / x

30.

U = ln ( 2xsiny ) , d³u / dx³ = ?

2 / x³

-3 / x⁴

4 / x⁵

-1 / x²

-5 / x⁶

31.

U = ln ( 2xsiny ) , d³u / dy³ = ?

2 ( cosy / siny + cos³y / sin³y )

-3 ( cosy / siny - cos³y / sin³y )

4x ( cosy / siny + cos³y / sin³y )

-5y ( cosy / siny - cos³y / sin³y )

-xy ( cosy / siny + cos³y / sin³y )

32.

U = e^2x+3y , d²u / dx² = 0

4e^2x+3y

5xe^2x+3y

-2e^2x+3y

6e^2x+3y

3ye^2x+3y

33.

U = 8x⁴y²+30x³y+100xy³+12x²y⁴ , du / dx = ?

32x³y²+90x²y+100y³+24xy⁴

33x³y²+89x²y-98y³+23xy⁴

-32x³y²+91x²y-98y³+23xy⁴

31x³y²-88x²y+96y³+22xy⁴

-31x³y²+92x²y-104y³+24xy⁴

34.

U = 8x⁴y²+30x³y+100xy³+12x²y⁴ , du / dy = ?

16x⁴y+30x³+300xy²+48x²y²

16x³y+30x²+200xy³+28x²y²

16x⁵y+30x⁴+100xy^-2+68x³y³

16x²y+30x^-2-300xy⁴+58x⁴y³

16x⁶y+30x^-4-400xy^-2+84x^-2y³

35.

U = 8x⁴y²+30x³y+100xy³+12x²y⁴ , d²u / dydx = ?

64x³y+90x²+300y²+96xy³

64x²y-90x³-200y²+86xy³

64x³y²+90x⁴-400y²+76xy³

54x³y+80x²-300y⁴+66xy⁴

74x³y+100x²+100y³-106xy²

36.

U = 8x⁴y²+30x³y+100xy³+12x²y⁴ , d²u / dy² = ?

16x⁴+600xy+144x²y²

18x³-500xy+124x³y²

17x⁴+600xy-244x³y²

15x⁵-650xy-134x⁴y²

19x⁴+550xy-214x⁴y²

37.

U = 8x⁴y²+30x³y+100xy³+12x²y⁴ , d²u / dx² = ?

96x²y²+180xy+24y⁴

95x²y²-190xy+34y⁴

94x²y²+210xy-14y⁴

93x²y²+200xy+44y⁴

92x²y²-170xy+55y⁴

38.

U = ln ( 2xsiny ) d²y / dx^{2 = ?}

-1 / x²

1 / x³

-1 / x

sinx / x²

-cosx / x²

39.

U = x²+y²+z² функцияның М ( 1; 1; 1 ) нүктесіндегі S = ( 1; 1; 1 ) векторының бағыты бойынша туындысын табыңыз

2√3

3√5

5√2

4√7

√8

40.

e^y- e^x + xy = 0 , du / dx = ?

e^x - y / e^y + x

e^x + y / e^y - x

e^y - x / e^x + y

e^y + x / e^y - y

e^y - y / e^x + x

41.

e^z + x²y + z + 5 = 0 , du / dx = ?

-2xy / e^z - 1

3xy / e^z - 1

-5xy / e^z + 2

4xy / e^z - 2

-xy / e^z + 3

42.

z = e^{-3√x²+5y²} , du / dx = ?

-2x / 3^{3√(x²+5y²)²} e^{-3√x²+5y²}

2+x / 3^{3√(x²+5y²)²}e^{-3√x²+5y²}

-2-x / 3^{3√(x²+5y²)²} e^{-3√x²+5y²}

4x / 5^{3√(x²+5y²)²}e^{-3√x²+5y²}

-5x+4 / 3^{3√(x²+5y²)²} e^{-3√x²+5y²}

43.

z = arctg √x / y , dz / dx = ?

1 / 2(x+y) √y/x

1 / 3(x-y) √y/x

1 / 4(x+y) √y/x

1 / 5(x-y) √y/x

1 / (x+y) √y/x

44.

U = x³+17xy+10x-6y , d²u / dxdy = ?

45.

U = 6x³+3xy+10x+2y , d²u / dx² = ?

36x

21y

16x

31y

26x

46.

U = x²+y , d²u / dydx = ?

-3

-2

47.

U = x³+17xy+10x-6y , d²u / dydx² = ?

48.

U = ln ( x³ + y² ) , du / dy = ?

3y² / x³+y³

4x⁴ / x³+y³

5y² / x²-y²

2x² / x³+y³

y² /x³-y³

49.

U = x⁴y³ , du / dx = ?

4x³y³

x³ / y³

3x³+y³

5x³y³

2x³-y³

50.

U = -e^2x+3y , du / dx = ?

3e^2x-3y

-2e^2x+3y

5e^2x-3y

-4e^2x-3y

6e^2x-3y

51.

U = -e^2x+3y , du / dy = ?

-3e^2x+3y

2e^2x-3y

-4e^2x+3y

5e^2x-3y

-e^2x+3y

52.

U = e^2x+3+y , d²u / dydx = ?

2e^2x+3+y

-5e^2x+3-y

6e^2x-3+y

-3e^2x+3+y

4e^2x-3-y

53.

U = cos ( 3x + 5y ) , du /dx = ?

-3sin(3x+5y)

4cos(3x-5y)

-5sin(3x+5y)

2cos(3x+5y)

-6sin(3x-5y)

54.

z =^{-3√x²+5y²} , du / dy = ?

-10y / 3^{-3√(x²+5y²)²}e^{-3√x²+5y²}

10+y / 3^{-3√(x²+5y²)²} e^{-3√x²+5y²}

10-y / 3^{-3√(x²+5y²)²} e^{-3√x²+5y²}

10+x / 3^{-3√(x²+5y²)²} e^{-3√x²+5y²}

-10x-y / 3^{-3√(x²+5y²)²} e^-3√x²+y²

55.

z =^{-3√x²+5y²} , du / dy = ?

-10y / 3^{-3√(x²+5y²)²}e^{-3√x²+5y²}

10+y / 3^{-3√(x²+5y²)²} e^{-3√x²+5y²}

10-y / 3^{-3√(x²+5y²)²} e^{-3√x²+5y²}

10+x / 3^{-3√(x²+5y²)²} e^{-3√x²+5y²}

-10x-y / 3^{-3√(x²+5y²)²} e^-3√x²+y²

56.

U = ln √xy + cosy , M_o( 1;1 ) , duM_o / dx = ?

0,5

-0,8

0,7

-0,4

0,3

57.

U = 2sinxtgy , du / dx = ?

2cosxtgx

3sinxctgy

4cosxctgy

2sinx + 3tgy

cosx - 4tgy

58.

e^z + x²y + z + 5 = 0 , dz / dy = ?

-x² / e^z+1

x³ / e^z-1

-2x² / e^z+2

x³ / e^z-5

-3x² / e^z+3

59.

z = f( x,y ) , d_xz = ?

df / dx dx

df / dx dy

df / dy + dx

df / dy dy

df / dx - dx

60.

dy - 2dx = 0 , y( x ) = ?

2x + C

x² / 2 + C

Cx²

x²+ C

C - √x

61.

dy - x⁴dx = 0 , y( x ) = ?

x⁵ / 5 +C

-x⁴ / 4 + C

x³ / 3 + C

-x² / 2 + C

x⁶ / 6 + C

62.

U = e^2x+3y , d²u / dy² = ?

9e^2x+3y

-8e^2x+3y

6e^2x+3y

-4e^2x+3y

5e^2x+3y

63.

U = √xy + cosx , M_o( 4;4 ) , du(M_o) / dy = ?

0,5

0,6

0,7

0,4

0,3

64.

dy + 2dx = 0 , y( 0 ) = 1 , y( x ) = ?

2x+1

3x-2

4x+3

x-4

5x+6

65.

dx - 3dy = 0 , y( x ) = ?

x / 3 +C

2x+C

x+C

3 / x +C

x² / C

66.

z = e^usinv , u = xy , v = x+y , dz / dy = ?

e^xy[xsin(x+y) + cos(x+y)]

e^x+y[ysin(x+y) - cos(x+y)]

e^x-y[xsin(x-y) + cos(x-y)]

e^x/y[ycos(x+y) + sin(x+y)]

e^xy[xsin(x+y) - cos(x-y)

67.

U = √xy + cosz , M_o( 1;1 ПИ/3 ) , du(M_o) / dz = ?

-0,8660

1,7574

-2,6014

3,5643

4,4872

68.

dy + 5dx = 0 , y( 0 ) = 3 , y( x ) = ?

-5x+3

6x+3

-4x+3

3x+3

-2x+3

69.

U = cosxtgy , du / dy = ?

cosx( 1 + tg²y )

sin( 1 - ctg²y )

sin ( 1 + tg²y )

cos³xtg²y

√cosx ( 1 - tg²y )

70.

U = ln ( 2xsiny ) , d³u / dx³ = ?

2 / x³

-3 / x⁴

4 / x⁵

-1 / x²

5 / x⁶

71.

U = ln ( 2xsiny ) , d³u / dy³ = ?

2( ctgy + ctg³y )

3( ctgy - ctg³y )

4( ctgy + ctg³y )

5 ( ctgy - ctg³y )

( tgy + tg³y )

72.

U = e^2x+3y, d²u / dx²

4e^2x+3y

3e^2x-3y

5e^2x+3y

2e^2x-3y

-e^3x+2y

73.

U = 9x⁴y² + 3x³y + 10xy³ - 2x²y⁴ , du / dx = ?

36x³y² + 9x²y + 30y³ - 4xy⁴

38x³y² + 11x²y + 32y³ - 3xy⁴

40x³y² + 13x²y + 34y³ - xy⁴

42x³y² + 15x²y + 36y³ - xy⁴

44x³y² + 17x²y + 38y³ + xy⁴

74.

z = 2x³ + 30xy + 100x + 12y , du / dx = ?

e^xy[ysin(x+y) + cos (x-y³)]

e^x+y[ysin(x+y) - cos (x-y³)]

e^x-y[ysinx(x-y³) + cos(x-y)]

e^x/y[ycos(x+y) + sin(x-y³)]

e^xy[xsin(x+y³) - cos(x-y)]

75.

U = 2x³+ 30xy + 100x + 12y , du / dx = ?

6x²+30y+100

5x²-31y+99

4x²-30y+12

6x²-30y+12

7x²+30y-12

76.

U = ln ( 2xsiny ) , d²u / dy² = ?

-1 - cos²y / sin²y

1 - cos²x / sin²x

-1 + cos²x / sin²y

1 - cos²y / sin²x

-1 + cos²y / sin²y

77.

U = 2x³ + 30xy + 100x + 12y , du / dy = ?

12 + 30x

13 + 29y

14 + 28xy

15 + 27x²

12 - 30x

100 %

матем2 1-модуль

Total questions: 77

Worksheet time: 39mins

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