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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
25 terms
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StudBud Administration
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This is a chapter review game for derivatives in a Calculus BC class.
Flashcards
25 cards
F
Practice quiz
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Host live
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Questions
25
Answers
1
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)
2
Find y' for y=sin
3
(x)tan(4x)
4sin3(x)sec2(4x)
sin2(x) [3cos(x)tan(4x) + 4sin(x)sec2(4x)]
1
sin2(x) + 4sin(x) - 3cos(x)
3
Find y' for y=sin
-1
(1-t)
1 / (2t-t2)
-1 / sqrt(2t-t2)
1
y' does not exist
4
If y=ln(x
2
), find y'.
2x2
2/x2
2
2/x
5
Find dy/dx for xsin(2y) = ycos(2x)
[-2ysin(2x)-sin(2y)]/[2xcos(2y)-cos(2x)]
dy/dx does not exist
[-2ysin(2x)-sin(2y)]*[cos(2x)]
1
6
The function y = (x)
2/3
fails to be differentiable at x=0, what type of problem is at x=0?
discontinuity
corner
cusp
vertical tangent
7
Use the limit of the difference quotient to determine the derivative of f(x)=x
3
3x2
x3+x+h
3x3
3x2+3h
8
Which of the following is not true about the derivatives of trig functions?
d/dx sec(x) = sec(x)tan(x)
d/dx cos(x) = -sin(x)
d/dx sin(x) = -cos(x)
d/dx tan(x) = sec2(x)
9
If f has a derivative at x=a, then f is continuous at x=a.
False
True
10
Who is responsible for discovering Calculus?
Gottfried Wilhelm von Leibniz
Issac Newton and Gottfried Wilhelm von Leibniz
Issac Newton
Mrs. Mascotti
11
For the graph below, does f'(0) exist?
yes
no
12
Which of the following is not true about the derivatives of inverse trig functions?
d/dx arcsin(x) = 1 / [sqrt(1-x2)]
d/dx arcsec(x) = 1 / [ |x|(x2-1) ]
d/dx arctan(x) = 1 / (1+x2)
d/dx arccos(x) = -1 / [sqrt(1-x2)]
13
Find an equation for the line tangent to the curve f(x)= (x
3
+1) / (2x) at x=1
y - 1 = 1/2(x - 1)
y = 1/2(x - 1)
y = 1/3(x + 3)
y - 2 = 1/3(x - 2)
14
Find y'', the second derivative, for y = x
3
-5x
2
+2
3x2-10x
6x-10
6
does not exist
15
Which of the following represents the power rule?
d/dx(xn) = (n-1)xn
d/dx(xn) = nxn+1
d/dx(xn) = (n) / (xn)
d/dx(xn) = nxn-1
16
Using implicit differentiation, find dy/dx for x
2
- xy + x
2
= 7
dy/dx = (y-2x) / (2y-x)
dy/dx = (y^2) / (-2x + y)
none of the above
dy/dx = 1
17
Find dr/dx for r = tan(2-x)
-sec2(2-x)
sec2(2-x)
sec2(2-x)*(2-x)
-tan(2-x)
18
What time is our cohort grad class to be at the school for commencement?
2:15 sharp.
1:30 sharp.
2 pm sharp.
1:45 pm sharp.
19
What rule is represented by d/dx (8) = 0?
constant rule
constant multiple rule
chain rule
sum rule
20
What word(s) does it say on Ms Lachance's bracelet (made by her daughter)?
Logville
I love derivatives
TrigTown
I love logs.
21
Which of the following is not true about the derivatives of exponential and log functions?
d/dx ex = ex
d/dx ln(x) = 1/x
d/dx ax = axln(a)
d/dx logax = ln(a) / x
22
Find f'(x) for f(x) = (x
2
+1)(x
3
+3)
5x4+3x2+6x
5x4+6x
5x4+3x
5x-3x2+6
23
Which of the following is not a derivative rule?
constant multiple rule
second derivative rule
difference rule
sum rule
24
The derivative of the function f(x) is represented by which of the following definitions?
limit as x approaches 0 of [f(x+h) - f(x)] / h
All of the above
limit as h approaches 0 of [f(x+h) - f(x)] / h
limit as h approaches 0 of [f(x+h) + f(x)] / x
25
Find y' for y=x
2
e
x
- xe
2x
3ex(x2+2x)-7e2x(2x+1)
ex(x2+2x)
1
ex(x2+2x)-e2x(2x+1)
