wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

AP Calc AB Unit 3 Test Review

Total questions: 116

Worksheet time: 10hrs 44mins

Name
Class
Date
1.
a)

A

b)

B

c)

C

d)

D

2.
a)

A

b)

B

c)

C

d)

D

3.
a)

A

b)

B

c)

C

d)

D

4.
a)

A

b)

B

c)

C

d)

D

5.
a)

A

b)

B

c)

C

d)

D

6.
a)

A

b)

B

c)

C

d)

D

7.
a)

A

b)

B

c)

C

d)

D

8.
a)

A

b)

B

c)

C

d)

D

9.
a)

A

b)

B

c)

C

d)

D

10.
a)

A

b)

B

c)

C

d)

D

11.
a)

A

b)

B

c)

C

d)

D

12.
a)

A

b)

B

c)

C

d)

D

13.
a)

A

b)

B

c)

C

d)

D

14.
a)

A

b)

B

c)

C

d)

D

15.
a)

A

b)

B

c)

C

d)

D

16.
a)

A

b)

B

c)

C

d)

D

17.
a)

A

b)

B

c)

C

d)

D

18.
a)

A

b)

B

c)

C

d)

D

19.

Find dy/dx in terms of x and y using the given equation

a)

(2x3+y)x+3y\frac{\left(-2x^3+y\right)}{x+3y}

b)

(2x2y2)x2+3y\frac{\left(-2x^2-y^2\right)}{x^2+3y}

c)

(2x3+y)x3y\frac{\left(2x^3+y\right)}{x-3y}

d)

(2x3y)x+3y\frac{\left(-2x^3-y\right)}{x+3y}

20.
Find dy/dx by Implicit Differentiation 
x3 +y3  = 36
a)
6 -x
b)
3x2 +3y2 
c)
−x2/y2
d)
0
21.
Find dy/dx at a given point.
a)
5/4
b)
4/5
c)
1
d)
-5
22.
a)
-3
b)
8
c)
0
d)
9
23.

Find  dydx\frac{dy}{dx}y2=10xy^2=10x  

a)

5y\frac{5}{y}  

b)

10y\frac{10}{y}  

c)

y25\frac{y^2}{5}  

d)

y210\frac{y^2}{10}  

24.

Find   dydx\frac{dy}{dx}  :  2x23y2=42x^2-3y^2=4  

a)

2xy\frac{2x}{y}  

b)

x3y\frac{x}{3y}  

c)

3y2x\frac{3y}{2x}  

d)

2x3y\frac{2x}{3y}  

25.

Find the derivative at a point.

a)

2/3

b)

-2/3

c)

1

d)

-1

26.

Find the derivative of x2+xy+y3=0x^2+xy+y^3=0  

a)

 2x1+3y2-\ \frac{2x}{1+3y^2}  

b)

x+3y22x+y-\frac{x+3y^2}{2x+y}  

c)

2x+yx+3y2-\frac{2x+y}{x+3y^2}  

d)

2xx+3y2-\frac{2x}{x+3y^2}  

27.

Find the derivative at a point.

a)

2/3

b)

-2/3

c)

1

d)

-1

28.

x2+xy+y2=9 @ (1,2)x^2+xy+y^2=9\ @\ \left(1,2\right)  Use implicit differentiation to write the equation of the tangent line to the curve at the given point.      

a)

y1=45(x2)y-1=\frac{-4}{5}\left(x-2\right)  

b)

y2=45(x1)y-2=\frac{-4}{5}\left(x-1\right)  

c)

y2=45(x1)y-2=\frac{4}{5}\left(x-1\right)  

d)

y+2=45(x+1)y+2=\frac{-4}{5}\left(x+1\right)  

29.

Find the derivative.

5y2=2x35y5y^2=2x^3-5y  

a)

dydx=5x2x2\frac{dy}{dx}=5x-\frac{2}{x^2}  

b)

dydx=6x210y5\frac{dy}{dx}=-\frac{6x^2}{10y-5}  

c)

dydx=7y2+5x\frac{dy}{dx}=-\frac{7}{y^2+5x}  

d)

dydx=6x210y+5\frac{dy}{dx}=\frac{6x^2}{10y+5}  

30.

Find the derivative of x2+xy+y3=0x^2+xy+y^3=0  

a)

 2x1+3y2-\ \frac{2x}{1+3y^2}  

b)

x+3y22x+y-\frac{x+3y^2}{2x+y}  

c)

2x+yx+3y2-\frac{2x+y}{x+3y^2}  

d)

2xx+3y2-\frac{2x}{x+3y^2}  

31.
Find the derivative:
y=5x2e3x
a)
y'=10xe3x(2x+3)
b)
y'=5xe3x(3x+2)
c)
y'=10ex3x(3x+2)
d)
y'=5xe3x(2x+3)
32.
Find the derivative of  f(x) = (x6 + 4)5
a)
f '(x) = 5x5(x4 + 4)4
b)
f '(x) = 6x5(x6 + 4)4
c)
f '(x) = 30x5(x6 + 4)4
d)
f '(x) = 30x6(x6 + 4)4
33.

Find the derivative for y=(1x2)5y=\left(1-x^2\right)^5  

a)

dydx=10x(1x2)6\frac{dy}{dx}=-10x\left(1-x^2\right)^6  

b)

dydx=10x(1x2)4\frac{dy}{dx}=10x\left(1-x^2\right)^4  

c)

dydx=10x(1x2)4\frac{dy}{dx}=-10x\left(1-x^2\right)^4  

d)

dydx=10(1x2)4\frac{dy}{dx}=10\left(1-x^2\right)^4  

34.

Find the derivative.

a)
b)
c)
d)
35.

Find the derivative for f(x)=12x2f\left(x\right)=\sqrt{1-2x^2}  

a)

f(x)=2x12x2f'\left(x\right)=\frac{-2x}{\sqrt{1-2x^2}}  

b)

f(x)=2x12x2f'\left(x\right)=\frac{2x}{\sqrt{1-2x^2}}  

c)

f(x)=2x12x2f'\left(x\right)=-2x\sqrt{1-2x^2}  

d)

f(x)=4x212x2f'\left(x\right)=\frac{-4x^2}{\sqrt{1-2x^2}}  

36.

Find the derivative.

a)
b)
c)
d)
37.

Find dpdq if p=1q+9\frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}}  

a)

12(q+9)32-\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}  

b)

12(q+9)32\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}  

c)

1(q+9)32-\frac{1}{\left(q+9\right)^{\frac{3}{2}}}  

d)

1q+9-\frac{1}{\sqrt{q+9}}  

38.

Find G'(2)

(a)  

39.

Find The Derivative at x=2

(a)  

40.

find y' for y= sin(2x2)

a)

4sin(2x2)

b)

4xcos(2x2)

c)

2xcos(2x2)

d)

xcos(4x2)

41.
a)
b)
c)
d)
42.
Find y' if y = tan(3x2+2).
a)
sec2(3x2+2)
b)
6xsec2(3x2+2)
c)
6xsec2x(3x2+2)
d)
sec2(6x)
43.

Find H'(1)

(a)  

44.
What is this expression equivalent to?
a)
f '(g'(x))
b)
f '(x)g'(x)
c)
f '(g(x))g'(x)
d)
f '(g(x)
45.


Find the derivative of following with respect to x:
f(x)=cos(x)f\left(x\right)=\sqrt{\cos\left(x\right)}  

a)

f '(x) = sin(x)2cos2(x)-\frac{\sin\left(x\right)}{2\cos^2\left(x\right)}  

b)

f '(x) = 2sin(x)cos(x)\frac{2\sin\left(x\right)}{\sqrt{\cos\left(x\right)}}  

c)

f '(x) = sin(x)2cos(x)-\frac{\sin\left(x\right)}{2\sqrt{\cos\left(x\right)}}  

d)

f '(x) = sin(x)cos(x)-\frac{\sin\left(x\right)}{\sqrt{\cos\left(x\right)}}  

46.
What is f'(x) if f(x) = cos(5x4)?
a)
f'(x) = sin(20x3)
b)
f'(x) = 20x3 sin(5x4)
c)
f'(x) = -sin(20x3)
d)
f'(x) = -20x3 sin(5x4)
47.

Differentiate y=e7xy=e^{7x}  

a)

dydx=7e7x\frac{\text{d}y}{\text{d}x}=7e^{7x}  

b)

dydx=7e7x\frac{\text{d}y}{\text{d}x}=-7e^{7x}  

c)

dydx=e7x7\frac{\text{d}y}{\text{d}x}=\frac{e^{7x}}{7}  

d)

dydx=7xe7x\frac{\text{d}y}{\text{d}x}=7xe^{7x}  

48.

dydxex=\frac{dy}{dx}e^{\sqrt{x}}=  

a)

exe^{\sqrt{x}}  

b)

xex\sqrt{x}e^{\sqrt{x}}  

c)

ex2x\frac{e^{\sqrt{x}}}{2\sqrt{x}}  

d)

exx\frac{e\sqrt{x}}{\sqrt{x}}  

49.

Find dydx\frac{\text{d}y}{\text{d}x}  for y=e3x2y=e^{3-x^2}  

a)

dydx=2xe3x2\frac{\text{d}y}{\text{d}x}=2xe^{3-x^2}  

b)

dydx=2xe3x2\frac{\text{d}y}{\text{d}x}=-2xe^{3-x^2}  

c)

dydx=(32x)e3x2\frac{\text{d}y}{\text{d}x}=\left(3-2x\right)e^{3-x^2}  

d)

dydx=x2e3x2\frac{\text{d}y}{\text{d}x}=-x^2e^{3-x^2}  

50.

Find the derivative for y=ln(3x2+x)y=\ln\left(3x^2+x\right)  

a)

dydx=3x+13x2+x\frac{\text{d}y}{\text{d}x}=\frac{3x+1}{3x^2+x}  

b)

dydx=6x+13x2+x\frac{\text{d}y}{\text{d}x}=\frac{6x+1}{3x^2+x}  

c)

dydx=6x3x2+x\frac{\text{d}y}{\text{d}x}=\frac{6x}{3x^2+x}  

d)

dydx=13x2+x\frac{\text{d}y}{\text{d}x}=\frac{1}{3x^2+x}  

51.

find y' for y=(e5x)+1

a)

5e5x+1

b)

e5x

c)

5e5x

d)

1

52.

Which of the following is the chain rule for derivatives utilizing the original function h(x) = f(g(x))

a)

h'(x)=(f'(g(x))(f'(x))

b)

h'(x)=(f'(g(x))(g(x))

c)

h'(x)=(f'(g(x))(f(x))

d)

h'(x)=(f'(g(x))(g'(x))

53.

Find the derivative of y=(x29)4y=\left(x^2-9\right)^4  

a)

dydx=8x(x29)3\frac{dy}{dx}=8x\left(x^2-9\right)^3  

b)

dydx=8(x29)3\frac{dy}{dx}=8\left(x^2-9\right)^3  

c)

dydx=8x(x29)4\frac{dy}{dx}=8x\left(x^2-9\right)^4  

d)

dydx=8(x29)4\frac{dy}{dx}=8\left(x^2-9\right)^4  

54.

ddxsin1(8x)\frac{d}{dx}\sin^{-1}\left(8x\right)

a)

8164x2\frac{8}{\sqrt[]{1-64x^2}}

b)

8164x2-\frac{8}{\sqrt[]{1-64x^2}}

c)

1164x2\frac{1}{\sqrt[]{1-64x^2}}

d)

1164x2-\frac{1}{\sqrt[]{1-64x^2}}

55.
a)
A
b)
B
c)
C
d)
D
56.
a)
A
b)
B
c)
C
d)
D
57.

1

a)

A

b)

B

c)

C

d)

D

58.
2
a)
A
b)
B
c)
C
d)
D
59.
5
a)
A
b)
B
c)
C
d)
D
60.
6
a)
A
b)
B
c)
C
d)
D
61.

Choose the best answer

a)

A

b)

B

c)

C

d)

D

62.

Choose the best answer

a)

A

b)

B

c)

C

d)

D

63.

Find the slope of the tangent line to the curve

xy3x3y=6xy^3-x^3y=6  at the point  (1, 2)\left(1,\ 2\right)  .

a)

25-\frac{2}{5}  

b)

1411-\frac{14}{11}  

c)

211-\frac{2}{11}  

d)

45\frac{4}{5}  

64.
a)

a

b)

b

c)

c

d)

d

e)

e

65.
a)

a

b)

b

c)

c

d)

d

e)

e

66.

What is the derivative of arcsin( x) ?

a)

arccos(x)

b)

11x2\frac{1}{\sqrt{1-x^2}}

c)

11+x2\frac{1}{1+x^2}

d)

- arccos(x)

67.

What is the derivative of arctan( x) ?

a)

arccos(x)

b)

11x2\frac{1}{\sqrt{1-x^2}}

c)

11+x2\frac{1}{1+x^2}

d)

- arccos(x)

68.

What is the derivative of arctan(3x)?

a)

31+9x2\frac{3}{1+9x^2}

b)

31+3x2\frac{3}{1+3x^2}

c)

31+9x2\frac{3}{\sqrt{1+9x^2}^{ }}

d)

11+9x2\frac{1}{1+9x^2}

69.

The expression below is the derivative of which function?

11+x2\frac{1}{1+x^2}  

a)

sin1(x)\sin^{-1}\left(x\right)  

b)

cos1(x)\cos^{-1}\left(x\right)  

c)

tan1(x)\tan^{-1}\left(x\right)  

d)

cot1(x)\cot^{-1}\left(x\right)  

e)

sec1(x)\sec^{-1}\left(x\right)  

70.

The expression below is the derivative of which function?

11x2\frac{-1}{\sqrt{1-x^2}}  

a)

sin1(x)\sin^{-1}\left(x\right)  

b)

cos1(x)\cos^{-1}\left(x\right)  

c)

tan1(x)\tan^{-1}\left(x\right)  

d)

cot1(x)\cot^{-1}\left(x\right)  

e)

csc1(x)\csc^{-1}\left(x\right)  

71.

The expression below is the derivative of which function?

11x2\frac{1}{\sqrt{1-x^2}}  

a)

sin1(x)\sin^{-1}\left(x\right)  

b)

cos1(x)\cos^{-1}\left(x\right)  

c)

sec1(x)\sec^{-1}\left(x\right)  

d)

cot1(x)\cot^{-1}\left(x\right)  

e)

csc1(x)\csc^{-1}\left(x\right)  

72.

dydt if y=cos10t+12\frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12}  Find

a)

510t+12sin10t+12\frac{-5}{\sqrt{10t+12}}\sin\sqrt{10t+12}  

b)

1210t+12sin10t+12\frac{-1}{2\sqrt{10t+12}}\sin\sqrt{10t+12}  

c)

sin10t+12-\sin\sqrt{10t+12}  

d)

sin(510t+12)-\sin\left(\frac{5}{\sqrt{10t+12}}\right)  

73.

dydx if y=e(79x)\frac{dy}{dx}\ if\ y=e^{\left(7-9x\right)}  Find

a)

9e(79x)-9e^{\left(7-9x\right)}  

b)

e9e^{-9}  

c)

9ln(79x)-9\ln\left(7-9x\right)  

d)

7e(79x)7e^{\left(7-9x\right)}  

74.

dydx if y=ln(ln2x)\frac{dy}{dx}\ if\ y=\ln\left(\ln2x\right)  Find

a)

1xln2x\frac{1}{x\ln2x}  

b)

1x\frac{1}{x}  

c)

12x\frac{1}{2x}  

d)

1ln2x\frac{1}{\ln2x}  

75.

dydxif y=ln2x\frac{dy}{dx}if\ y=\ln2x  Find

a)

1x-\frac{1}{x}  

b)

12x\frac{1}{2x}  

c)

1x\frac{1}{x}  

d)

12x\frac{-1}{2x}  

76.

dydx if y=(2x2+4)3\frac{dy}{dx}\ if\ y=\left(2x^2+4\right)^3  Find

a)

(12x+4)(2x2+4)2\left(12x+4\right)\left(2x^2+4\right)^2  

b)

3(2x2+4)23\left(2x^2+4\right)^2  

c)

12x(2x2+4)212x\left(2x^2+4\right)^2  

d)

12(2x2+4)212\left(2x^2+4\right)^2  

77.

What is the derivative of f(g(x))f(g(x)) with respect to x, where f(x)=x2f\left(x\right)=x^2 and g(x)=sin(x)g(x)=\sin(x) ?

a)

2cos(x)sin(x)2\cos(x)\sin(x)

b)

2cos2(x)2\cos^2(x)

c)

2xsin(x)cos(x)2x\sin(x)\cos(x)

d)

2sin(x)cos(x)2\sin(x)\cos(x)

78.

What is the derivative of cos(lnx)\cos\left(\ln x\right)

a)

sin(ln(x))x2-\frac{\sin(\ln(x))}{x^2}

b)

cos(ln(x))x\frac{\cos(\ln(x))}{x}

c)

sin(ln(x))x-\frac{\sin(\ln(x))}{x}

d)

sin(x)x-\frac{\sin(x)}{x}

79.

Find the derivative of ex3e^{x^3}

a)

3x2 ex33x^{2\ }e^{x^3}

b)

3x2 ex3+ex33x^{2\ }e^{x^3}+e^{x^3}

c)

3x2ex3+x33x^2e^{x^3}+x^3

d)

3x2ex3ex33x^2e^{x^3}-e^{x^3}

80.

Differentiate sin(lnx)\sin\left(\ln x\right)

a)

(cos(ln(x))x\frac{\left(\cos(\ln(x)\right)}{x}

b)

sin(ln(x))x\frac{\sin(\ln(x))}{x}

c)

cos(x)ln(x)\frac{\cos(x)}{\ln\left(x\right)}

d)

cos(x)x\frac{\cos(x)}{x}

81.

Find the derivative of:
f(x) = (x+1)6

a)
12(x2 + 1)6
b)
12x(x2 + 1)6
c)
12x(x2 + 1)5
d)
12(x2 + 1)5
82.

Differentiate f(x)=194x2f\left(x\right)=\frac{1}{9-4x^2}

a)

8x(94x2)2\frac{8x}{\left(9-4x^2\right)^2}

b)

8x(94x2)2\frac{-8x}{\left(9-4x^2\right)^2}

c)

8x(94x2)2-\frac{8x}{\left(9-4x^2\right)^{-2}}

d)

8x(94x2)2-8x(9-4x^2)^2

83.

ddxln(x3+2x+1)=\frac{d}{dx}\ln\left(x^3+2x+1\right)=  

a)

13x2+2\frac{1}{3x^2+2}  

b)

1x3+2x+1\frac{1}{x^3+2x+1}  

c)

3x2+2x3+2x+1\frac{3x^2+2}{x^3+2x+1}  

d)

5x+3\frac{5}{x+3}  

84.

ddxcos3(2x)=\frac{d}{dx}\cos^3\left(2x\right)=  

a)

3cos2(x)sinx-3\cos^2\left(x\right)\sin x  

b)

3sin2(2x)-3\sin^2\left(2x\right)  

c)

6cos2(2x)sin(2x)-6\cos^2\left(2x\right)\sin\left(2x\right)  

d)

6sin2(2x)-6\sin^2\left(2x\right)  

e)

3cos2(2x)sin(2x)-3\cos^2\left(2x\right)\sin\left(2x\right)  

85.
a)

A

b)

B

c)

C

d)

D

e)

E

86.
Find h'(3)
a)
-2
b)
0
c)
1
d)
3
87.

Can a function be continuous but not differentiable?

a)

Yes

b)

No

88.

If a function is differentiable, it is also continuous.

a)

Yes

b)

No

c)

It all depends on the function in question.

89.

The function shown

a)

is continuous at x = 2

b)

is differentiable at x = 2

c)

has a limit that exists at x = 2

d)

exists at x = 2

90.

Is the function continuous, differentiable, both, or neither?

a)

continuous

b)

differentiable

c)

both

d)

neither

91.

Where is the function shown in the graph not differentiable?

a)

x = -2, -1, 0, 1

b)

x = -2, -1, 1

c)

x = -2, -1

d)

x = -1,

92.

Find f "'(x) when

f(x)=10x5 +3x4 -5x3 +2x2 -10x+6

a)

200x3+36x2 -30x+4

b)

600x2 +72x -26

c)

600x2 +72x -30

d)

600x2 +72x -36

93.
Find the second derivative of the function:
f (x) =  2x - 5x6
a)
f ''(x)= 2 - 30x
b)
f ''(x) =  2-30x5
c)
f ''(x) = -30x5
d)
f ''(x) = -150x4
94.

Find the second derivative (by Implicit Differentiation) of

8x2 + 16y2 = 144 at (1,1).

a)

34\frac{3}{4}

b)

34\frac{-3}{4}

c)

14\frac{1}{4}

d)

14\frac{-1}{4}

95.

Find y'' for y = 3x2 + 5x + cos x

a)

f''(x) = 6x + cos x

b)

f''(x) = 3x + 5 - sin x

c)

f''(x) = 6x + 5 + sin x

d)

f''(x) = 6 - cos x

96.

Find the derivative of

f(x)=(x3+1)7f\left(x\right)=\left(x^3+1\right)^7  

a)

7(3x2+1)67\left(3x^2+1\right)^6  

b)

7(x3+1)6(3x2)7\left(x^3+1\right)^6\left(3x^2\right)  

c)

21x221x^2  

d)

21x2(x18)21x^2\left(x^{18}\right)  

97.

Find the derivative of

f(x)=x2+8f\left(x\right)=\sqrt{x^2+8}  

a)

12x2+8\frac{1}{2\sqrt[]{x^2+8}}  

b)

12(x2+8)32(2x)\frac{1}{2}\left(x^2+8\right)^{\frac{3}{2}}\left(2x\right)  

c)

x(x2+8)12x\left(x^2+8\right)^{\frac{1}{2}}  

d)

xx2+8\frac{x}{\sqrt[]{x^2+8}}  

98.

Find the derivative of

y=(e2x+ex)12y=\left(e^{2x}+e^x\right)^{\frac{1}{2}}

a)

12(e2x+ex)12\frac{1}{2}\left(e^{2x}+e^x\right)^{-\frac{1}{2}}  

b)

12(e2x+ex)12+(e2x+ex)\frac{1}{2}\left(e^{2x}+e^x\right)^{-\frac{1}{2}}+\left(e^{2x}+e^x\right)  

c)

12(e2x+ex)12(2e2x+ex)\frac{1}{2}\left(e^{2x}+e^x\right)^{-\frac{1}{2}}\left(2e^{2x}+e^x\right)  

d)

12(e2x+ex)12(2e2x+1)\frac{1}{2}\left(e^{2x}+e^x\right)^{\frac{1}{2}}\left(2e^{2x}+1\right)  

99.

Find the derivative of

y=etanxy=e^{\tan x}

a)

etanxe^{\tan x}  

b)

etanx(sec2x)e^{\tan x}\left(\sec^2x\right)  

c)

etanx(sec2x)e^{\tan x}\left(-\sec^2x\right)  

d)

etanx(cot x)e^{\tan x}\left(\cot\ x\right)  

100.

Find the second derivative of y = 5x33x2+6x  1 5x^3-3x^2+6x\ -\ 1\  

a)

y = 15x2  6x +6 y'\ =\ 15x^2\ -\ 6x\ +6\  

b)

y = 15x26x +6y''\ =\ 15x^2-6x\ +6  

c)

y = 30x  6 y'\ =\ 30x\ -\ 6\  

d)

y = 30x  6y''\ =\ 30x\ -\ 6  

101.

Let f be the function f(x) = 32x +x3 f\left(x\right)\ =\ -\frac{32}{x}\ +x^{3\ }  . Find f''(x) when x = 2

a)

-8

b)

4

c)

5

d)

20

102.

If y = cos(x) - ln(2x), then y''' =

a)

y = sin(x)  2x3y'''\ =\ \sin\left(x\right)\ -\ \frac{2}{x^3}  

b)

y = sin(x)  2x3y'''\ =\ -\sin\left(x\right)\ -\ \frac{2}{x^3}  

c)

y = sin(x) + 2x3y'''\ =\ -\sin\left(x\right)\ +\ \frac{2}{x^3}  

d)

y = sin(x) + 2x3y'''\ =\ -\sin\left(x\right)\ +\ \frac{2}{x^3}  

103.

If y = x42x3+3x 1 y'\ =\ x^4-2x^3+3x\ -1\  then y''' evaluated at x = 2 is equal to what?

a)

11

b)

48

c)

24

d)

26

104.

Find the second derivative of y = 5x33x2+6x  1 5x^3-3x^2+6x\ -\ 1\  

a)

y = 15x2  6x +6 y'\ =\ 15x^2\ -\ 6x\ +6\  

b)

y = 15x26x +6y''\ =\ 15x^2-6x\ +6  

c)

y = 30x  6 y'\ =\ 30x\ -\ 6\  

d)

y = 30x  6y''\ =\ 30x\ -\ 6  

105.

If x3+3xy + 2y3=17 x^3+3xy\ +\ 2y^3=17\  find y'

a)

x2+yx+2y2-\frac{x^2+y}{x+2y^2}  

b)

x2+yx+y2-\frac{x^2+y}{x+y^2}  

c)

x2+yx+2y-\frac{x^2+y}{x+2y}  

d)

x2+y2y2-\frac{x^2+y}{2y^2}  

e)

x21+2y2-\frac{x^2}{1+2y^2}  

106.

If y3+y = x2y^3+y\ =\ x^2   find y'

a)

y' = 0

b)

y' = x2\frac{x}{2}  

c)

y' = 2x3y2\frac{2x}{3y^2}  

d)

y' = 2x3y22x-3y^2  

e)

y' = 2x1+3y2\frac{2x}{1+3y^2}  

107.

Find the 3rd derivative if

y=3x412x3+11x28x+10y=3x^4-12x^3+11x^2-8x+10  

a)

d3ydx3=36x272x+22\frac{d^3y}{dx^3}=36x^2-72x+22  

b)

d3ydx3=12x336x2+22x8\frac{d^3y}{dx^3}=12x^3-36x^2+22x-8  

c)

d3ydx3=72x  72\frac{d^3y}{dx^3}=72x\ -\ 72  

d)

d3ydx3=72\frac{d^3y}{dx^3}=72  

e)

d3ydx3=0\frac{d^3y}{dx^3}=0  

108.

Find the 15th derivative if

y=3x412x3+11x28x+10y=3x^4-12x^3+11x^2-8x+10  

a)

d15ydx15=36x272x+22\frac{d^{15}y}{dx^{15}}=36x^2-72x+22  

b)

d15ydx15=12x336x2+22x8\frac{d^{15}y}{dx^{15}}=12x^3-36x^2+22x-8  

c)

d15ydx15=72x  72\frac{d^{15}y}{dx^{15}}=72x\ -\ 72  

d)

d15ydx15=72\frac{d^{15}y}{dx^{15}}=72  

e)

d15ydx15=0\frac{d^{15}y}{dx^{15}}=0  

109.

Find the 2nd Derivative of

y=(3x4)5y=\left(3x-4\right)^5  

a)

y = 5(3x4)4y''\ =\ 5\left(3x-4\right)^4  

b)

y = 15(3x4)4y''\ =\ 15\left(3x-4\right)^4  

c)

y = 60(3x4)3y''\ =\ 60\left(3x-4\right)^3  

d)

y = 180(3x4)3y''\ =\ 180\left(3x-4\right)^3  

e)

y = 180(3x4)4y''\ =\ 180\left(3x-4\right)^4  

110.

Find the 2nd derivative 0f

y=3x2+12x311x4812y=-\frac{3}{x^2}+\frac{12}{x^3}-\frac{11}{x^4}-\frac{8}{12}  

a)

d2ydx2=18x4144x5+220x6\frac{d^2y}{dx^2}=\frac{18}{x^4}-\frac{144}{x^5}+\frac{220}{x^6}  

b)

d2ydx2=18x4+144x5220x6\frac{d^2y}{dx^2}=-\frac{18}{x^4}+\frac{144}{x^5}-\frac{220}{x^6}  

c)

d2ydx2=6x3+36x444x5\frac{d^2y}{dx^2}=-\frac{6}{x^3}+\frac{36}{x^4}-\frac{44}{x^5}  

111.
Find the second derivative of the function:
f (x) =  2x - 5x6
a)
f ''(x)= 2 - 30x
b)
f ''(x) =  2-30x5
c)
f ''(x) = -30x5
d)
f ''(x) = -150x4
112.
d/dx (sin3(4x-6)) = ?
a)
-24x-5 ⋅ cos (4x-6) ⋅ 3sin2(4x-6)
b)
-24x-7 ⋅ cos (4x-6) ⋅ 3sin2(4x-6)
c)
-24x-7 ⋅ 3cos2(4x-6)
d)
3cos2(-24x-5)
113.
a)

-2

b)

-2/3

c)

2/3

d)

2

114.

a)

A

b)

B

c)

C

d)

D

e)

E

115.
a)

A

b)

B

c)

C

d)

D

116.
a)

A

b)

B

c)

C

d)

D

e)

E