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