WorksheetsAP Calc AB Unit 3 Test Review
Total questions: 116
Worksheet time: 10hrs 44mins
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
Find dy/dx in terms of x and y using the given equation
x+3y(−2x3+y)
x2+3y(−2x2−y2)
x−3y(2x3+y)
x+3y(−2x3−y)
x3 +y3 = 36
Find dxdy : y2=10x
y5
y10
5y2
10y2
Find dxdy : 2x2−3y2=4
y2x
3yx
2x3y
3y2x
Find the derivative at a point.
2/3
-2/3
1
-1
Find the derivative of x2+xy+y3=0
− 1+3y22x
−2x+yx+3y2
−x+3y22x+y
−x+3y22x
Find the derivative at a point.
2/3
-2/3
1
-1
x2+xy+y2=9 @ (1,2) Use implicit differentiation to write the equation of the tangent line to the curve at the given point.
y−1=5−4(x−2)
y−2=5−4(x−1)
y−2=54(x−1)
y+2=5−4(x+1)
Find the derivative.
5y2=2x3−5y
dxdy=5x−x22
dxdy=−10y−56x2
dxdy=−y2+5x7
dxdy=10y+56x2
Find the derivative of x2+xy+y3=0
− 1+3y22x
−2x+yx+3y2
−x+3y22x+y
−x+3y22x
y=5x2e3x
Find the derivative for y=(1−x2)5
dxdy=−10x(1−x2)6
dxdy=10x(1−x2)4
dxdy=−10x(1−x2)4
dxdy=10(1−x2)4
Find the derivative.
Find the derivative for f(x)=1−2x2
f′(x)=1−2x2−2x
f′(x)=1−2x22x
f′(x)=−2x1−2x2
f′(x)=1−2x2−4x2
Find the derivative.
Find dqdp if p=q+91
−2(q+9)231
2(q+9)231
−(q+9)231
−q+91
Find G'(2)
(a)
Find The Derivative at x=2
(a)
find y' for y= sin(2x2)
4sin(2x2)
4xcos(2x2)
2xcos(2x2)
xcos(4x2)
Find H'(1)
(a)
Find the derivative of following with respect to x:
f(x)=cos(x)
f '(x) = −2cos2(x)sin(x)
f '(x) = cos(x)2sin(x)
f '(x) = −2cos(x)sin(x)
f '(x) = −cos(x)sin(x)
Differentiate y=e7x
dxdy=7e7x
dxdy=−7e7x
dxdy=7e7x
dxdy=7xe7x
dxdyex=
ex
xex
2xex
xex
Find dxdy for y=e3−x2
dxdy=2xe3−x2
dxdy=−2xe3−x2
dxdy=(3−2x)e3−x2
dxdy=−x2e3−x2
Find the derivative for y=ln(3x2+x)
dxdy=3x2+x3x+1
dxdy=3x2+x6x+1
dxdy=3x2+x6x
dxdy=3x2+x1
find y' for y=(e5x)+1
5e5x+1
e5x
5e5x
1
Which of the following is the chain rule for derivatives utilizing the original function h(x) = f(g(x))
h'(x)=(f'(g(x))(f'(x))
h'(x)=(f'(g(x))(g(x))
h'(x)=(f'(g(x))(f(x))
h'(x)=(f'(g(x))(g'(x))
Find the derivative of y=(x2−9)4
dxdy=8x(x2−9)3
dxdy=8(x2−9)3
dxdy=8x(x2−9)4
dxdy=8(x2−9)4
dxdsin−1(8x)
1−64x28
−1−64x28
1−64x21
−1−64x21
1
A
B
C
D
Choose the best answer
A
B
C
D
Choose the best answer
A
B
C
D
Find the slope of the tangent line to the curve
xy3−x3y=6 at the point (1, 2) .−52
−1114
−112
54
a
b
c
d
e
a
b
c
d
e
What is the derivative of arcsin( x) ?
arccos(x)
1−x21
1+x21
- arccos(x)
What is the derivative of arctan( x) ?
arccos(x)
1−x21
1+x21
- arccos(x)
What is the derivative of arctan(3x)?
1+9x23
1+3x23
1+9x23
1+9x21
The expression below is the derivative of which function?
sin−1(x)
cos−1(x)
tan−1(x)
cot−1(x)
sec−1(x)
The expression below is the derivative of which function?
sin−1(x)
cos−1(x)
tan−1(x)
cot−1(x)
csc−1(x)
The expression below is the derivative of which function?
sin−1(x)
cos−1(x)
sec−1(x)
cot−1(x)
csc−1(x)
dtdy if y=cos10t+12 Find
10t+12−5sin10t+12
210t+12−1sin10t+12
−sin10t+12
−sin(10t+125)
dxdy if y=e(7−9x) Find
−9e(7−9x)
e−9
−9ln(7−9x)
7e(7−9x)
dxdy if y=ln(ln2x) Find
xln2x1
x1
2x1
ln2x1
dxdyif y=ln2x Find
−x1
2x1
x1
2x−1
dxdy if y=(2x2+4)3 Find
(12x+4)(2x2+4)2
3(2x2+4)2
12x(2x2+4)2
12(2x2+4)2
What is the derivative of f(g(x)) with respect to x, where f(x)=x2 and g(x)=sin(x) ?
2cos(x)sin(x)
2cos2(x)
2xsin(x)cos(x)
2sin(x)cos(x)
What is the derivative of cos(lnx)
−x2sin(ln(x))
xcos(ln(x))
−xsin(ln(x))
−xsin(x)
Find the derivative of ex3
3x2 ex3
3x2 ex3+ex3
3x2ex3+x3
3x2ex3−ex3
Differentiate sin(lnx)
x(cos(ln(x))
xsin(ln(x))
ln(x)cos(x)
xcos(x)
Find the derivative of:
f(x) = (x2 +1)6
Differentiate f(x)=9−4x21
(9−4x2)28x
(9−4x2)2−8x
−(9−4x2)−28x
−8x(9−4x2)2
dxdln(x3+2x+1)=
3x2+21
x3+2x+11
x3+2x+13x2+2
x+35
dxdcos3(2x)=
−3cos2(x)sinx
−3sin2(2x)
−6cos2(2x)sin(2x)
−6sin2(2x)
−3cos2(2x)sin(2x)
A
B
C
D
E
Can a function be continuous but not differentiable?
Yes
No
If a function is differentiable, it is also continuous.
Yes
No
It all depends on the function in question.
The function shown
is continuous at x = 2
is differentiable at x = 2
has a limit that exists at x = 2
exists at x = 2
Is the function continuous, differentiable, both, or neither?
continuous
differentiable
both
neither
Where is the function shown in the graph not differentiable?
x = -2, -1, 0, 1
x = -2, -1, 1
x = -2, -1
x = -1,
Find f "'(x) when
f(x)=10x5 +3x4 -5x3 +2x2 -10x+6
200x3+36x2 -30x+4
600x2 +72x -26
600x2 +72x -30
600x2 +72x -36
f (x) = 2x - 5x6
Find the second derivative (by Implicit Differentiation) of
8x2 + 16y2 = 144 at (1,1).
43
4−3
41
4−1
Find y'' for y = 3x2 + 5x + cos x
f''(x) = 6x + cos x
f''(x) = 3x + 5 - sin x
f''(x) = 6x + 5 + sin x
f''(x) = 6 - cos x
Find the derivative of
f(x)=(x3+1)77(3x2+1)6
7(x3+1)6(3x2)
21x2
21x2(x18)
Find the derivative of
f(x)=x2+8
2x2+81
21(x2+8)23(2x)
x(x2+8)21
x2+8x
Find the derivative of
y=(e2x+ex)2121(e2x+ex)−21
21(e2x+ex)−21+(e2x+ex)
21(e2x+ex)−21(2e2x+ex)
21(e2x+ex)21(2e2x+1)
Find the derivative of
y=etanxetanx
etanx(sec2x)
etanx(−sec2x)
etanx(cot x)
Find the second derivative of y = 5x3−3x2+6x − 1
y′ = 15x2 − 6x +6
y′′ = 15x2−6x +6
y′ = 30x − 6
y′′ = 30x − 6
Let f be the function f(x) = −x32 +x3 . Find f''(x) when x = 2
-8
4
5
20
If y = cos(x) - ln(2x), then y''' =
y′′′ = sin(x) − x32
y′′′ = −sin(x) − x32
y′′′ = −sin(x) + x32
y′′′ = −sin(x) + x32
If y′ = x4−2x3+3x −1 then y''' evaluated at x = 2 is equal to what?
11
48
24
26
Find the second derivative of y = 5x3−3x2+6x − 1
y′ = 15x2 − 6x +6
y′′ = 15x2−6x +6
y′ = 30x − 6
y′′ = 30x − 6
If x3+3xy + 2y3=17 find y'
−x+2y2x2+y
−x+y2x2+y
−x+2yx2+y
−2y2x2+y
−1+2y2x2
If y3+y = x2 find y'
y' = 0
y' = 2x
y' = 3y22x
y' = 2x−3y2
y' = 1+3y22x
Find the 3rd derivative if
y=3x4−12x3+11x2−8x+10dx3d3y=36x2−72x+22
dx3d3y=12x3−36x2+22x−8
dx3d3y=72x − 72
dx3d3y=72
dx3d3y=0
Find the 15th derivative if
y=3x4−12x3+11x2−8x+10dx15d15y=36x2−72x+22
dx15d15y=12x3−36x2+22x−8
dx15d15y=72x − 72
dx15d15y=72
dx15d15y=0
Find the 2nd Derivative of
y=(3x−4)5y′′ = 5(3x−4)4
y′′ = 15(3x−4)4
y′′ = 60(3x−4)3
y′′ = 180(3x−4)3
y′′ = 180(3x−4)4
Find the 2nd derivative 0f
y=−x23+x312−x411−128
dx2d2y=x418−x5144+x6220
dx2d2y=−x418+x5144−x6220
dx2d2y=−x36+x436−x544
f (x) = 2x - 5x6
-2
-2/3
2/3
2
A
B
C
D
E
A
B
C
D
A
B
C
D
E
