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Chapter 3& 4 Review: Derivatives Flashcards | StudBud
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Chapter 3& 4 Review: Derivatives
Chapter 3& 4 Review: Derivatives
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This is a chapter review game for derivatives in an AB Calculus class.
Flashcards
29 cards
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Practice quiz
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Questions
29
Answers
1
Which of the following is not true about the derivatives of inverse trig functions?
d/dx arctan(x) = 1 / (1+x2)
d/dx arcsin(x) = 1 / [sqrt(1-x2)]
d/dx arccos(x) = -1 / [sqrt(1-x2)]
d/dx arcsec(x) = 1 / [ |x|(x2-1) ]
2
Which of the following represents the power rule?
d/dx(xn) = (n) / (xn)
d/dx(xn) = nxn-1
d/dx(xn) = (n-1)xn
d/dx(xn) = nxn+1
3
Using left and right handed derivatives, does the derivative at x=0 exist for the function...
yes, y'(0) = 0
yes, because the function is defined at x=0
yes, y'(0) = 2
No, f'(0) does not exist
4
The function y = (x)
2/3
fails to be differentiable at x=0, what type of problem is at x=0?
cusp
corner
discontinuity
vertical tangent
5
Using implicit differentiation, find dy/dx for x
2
- xy + x
2
= 7
none of the above
dy/dx = 1
dy/dx = (y^2) / (-2x + y)
dy/dx = (y-2x) / (2y-x)
6
Which of the following is not true about the derivatives of exponential and log functions?
d/dx ax = axln(a)
d/dx ex = ex
d/dx logax = ln(a) / x
d/dx ln(x) = 1/x
7
Find an equation for the line tangent to the curve f(x)= (x
3
+1) / (2x) at x=1
y = 1/3(x + 3)
y = 1/2(x - 1)
y - 1 = 1/2(x - 1)
y - 2 = 1/3(x - 2)
8
All of the following are proper notations for the derivative f(x), f(x) is replaceable by y
y'
dy/dx
d/dx
df/dx
9
Who is responsible for discovering Calculus?
Issac Newton
Mrs. Mascotti
Issac Newton and Gottfried Wilhelm von Leibniz
Gottfried Wilhelm von Leibniz
10
Find y' for y=x
2
e
x
- xe
2x
1
ex(x2+2x)-e2x(2x+1)
ex(x2+2x)
3ex(x2+2x)-7e2x(2x+1)
11
Use the limit of the difference quotient to determine the derivative of f(x)=x
3
3x2
3x2+3h
x3+x+h
3x3
12
The derivative of the function f(x) is represented by which of the following definitions?
limit as h approaches 0 of [f(x+h) + f(x)] / x
limit as x approaches 0 of [f(x+h) - f(x)] / h
limit as h approaches 0 of [f(x+h) - f(x)] / h
All of the above
13
Find y'', the second derivative, for y = x
3
-5x
2
+2
3x2-10x
6x-10
6
does not exist
14
If a particle's position is represented by s(t)=(t
2
-4t+3) / (t+1), find the velocity at t=2
9
2/9
1/9
1/3
15
Find dy/dx for xsin(2y) = ycos(2x)
[-2ysin(2x)-sin(2y)]/[2xcos(2y)-cos(2x)]
1
dy/dx does not exist
[-2ysin(2x)-sin(2y)]*[cos(2x)]
16
Which of the following is not a derivative rule?
sum rule
second derivative rule
difference rule
constant multiple rule
17
Find y' for y=sin
3
(x)tan(4x)
1
sin2(x) + 4sin(x) - 3cos(x)
4sin3(x)sec2(4x)
sin2(x) [3cos(x)tan(4x) + 4sin(x)sec2(4x)]
18
Which of the following is not true about the derivatives of trig functions?
d/dx sec(x) = sec(x)tan(x)
d/dx sin(x) = -cos(x)
d/dx cos(x) = -sin(x)
d/dx tan(x) = sec2(x)
19
Which of the following is true about the domains of a function and its derivative f'(x)?
domain f(x) is greater than or equal to the domain f'(x)
domain f(x) is less than or equal to the domain f'(x)
20
Find f'(x) for f(x) = (x
2
+1)(x
3
+3)
5x4+6x
5x-3x2+6
5x4+3x2+6x
5x4+3x
21
Find y' for y=sin
-1
(1-t)
y' does not exist
-1 / sqrt(2t-t2)
1 / (2t-t2)
1
22
Find dy/dx for y = (x) / (1 + cos(x))
[1-cos(x)+3xsin(x)] / [1+2cos(x)+cos2(x)]
[1] / [1+2cos(x)+cos2(x)]
[1+cos(x)+xsin(x)]
[1+cos(x)+xsin(x)] / [1+2cos(x)+cos2(x)]
23
If a particle's position is represented by s(t)=t
2
-4t+3, find the acceleration at t=3
6
2
1/2
does not exist
24
For the graph below, does f'(0) exist?
no
yes
25
Find dr/dx for r = tan(2-x)
-tan(2-x)
sec2(2-x)*(2-x)
sec2(2-x)
-sec2(2-x)
26
If y=ln(x
2
), find y'.
2/x2
2
2x2
2/x
27
If f has a derivative at x=a, then f is continuous at x=a.
False
True
28
Which of the following is not true about the derivatives of trig functions?
d/dx sin(x) = cos(x)
d/dx cot(x) = -csc2(x)
d/dx csc(x) = csc(x)cot(x)
d/dx tan(x) = sec2(x)
29
What rule is represented by d/dx (8) = 0?
chain rule
sum rule
constant multiple rule
constant rule
