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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
30 terms
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This is a chapter review game for derivatives in a Calculus BC class.
Flashcards
30 cards
F
Practice quiz
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Host live
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Questions
30
Answers
1
Use the limit of the difference quotient to determine the derivative of f(x)=x
3
x3+x+h
3x2
3x3
3x2+3h
2
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 arctan(x) = 1 / (1+x2)
d/dx arcsec(x) = 1 / [ |x|(x2-1) ]
3
Which of the following is not true about the derivatives of exponential and log functions?
d/dx logax = ln(a) / x
d/dx ex = ex
d/dx ax = axln(a)
d/dx ln(x) = 1/x
4
Who is responsible for discovering Calculus?
Issac Newton
Issac Newton and Gottfried Wilhelm von Leibniz
Gottfried Wilhelm von Leibniz
Mrs. Mascotti
5
Find y' for y=x
2
e
x
- xe
2x
ex(x2+2x)-e2x(2x+1)
1
3ex(x2+2x)-7e2x(2x+1)
ex(x2+2x)
6
Find dr/dx for r = tan(2-x)
-sec2(2-x)
-tan(2-x)
sec2(2-x)*(2-x)
sec2(2-x)
7
The derivative of the function f(x) is represented by which of the following definitions?
All of the above
limit as h approaches 0 of [f(x+h) - f(x)] / h
limit as x approaches 0 of [f(x+h) - f(x)] / h
limit as h approaches 0 of [f(x+h) + f(x)] / x
8
If a particle's position is represented by s(t)=t
2
-4t+3, find the acceleration at t=3
does not exist
1/2
2
6
9
For the graph below, does f'(0) exist?
no
yes
10
Which of the following is not a derivative rule?
sum rule
second derivative rule
difference rule
constant multiple rule
11
If y=ln(x
2
), find y'.
2
2x2
2/x
2/x2
12
Which of the following represents the power rule?
d/dx(xn) = nxn+1
d/dx(xn) = (n) / (xn)
d/dx(xn) = nxn-1
d/dx(xn) = (n-1)xn
13
If f has a derivative at x=a, then f is continuous at x=a.
False
True
14
Find f'(x) for f(x) = (x
2
+1)(x
3
+3)
5x4+3x
5x-3x2+6
5x4+3x2+6x
5x4+6x
15
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 sec(x) = sec(x)tan(x)
d/dx tan(x) = sec2(x)
16
The function y = (x)
2/3
fails to be differentiable at x=0, what type of problem is at x=0?
corner
cusp
discontinuity
vertical tangent
17
Find y'', the second derivative, for y = x
3
-5x
2
+2
6
6x-10
does not exist
3x2-10x
18
Using implicit differentiation, find dy/dx for x
2
- xy + x
2
= 7
dy/dx = (y-2x) / (2y-x)
dy/dx = 1
dy/dx = (y^2) / (-2x + y)
none of the above
19
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
20
Find y' for y=sin
3
(x)tan(4x)
sin2(x) [3cos(x)tan(4x) + 4sin(x)sec2(4x)]
4sin3(x)sec2(4x)
1
sin2(x) + 4sin(x) - 3cos(x)
21
Find an equation for the line tangent to the curve f(x)= (x
3
+1) / (2x) at x=1
y = 1/2(x - 1)
y - 1 = 1/2(x - 1)
y = 1/3(x + 3)
y - 2 = 1/3(x - 2)
22
What rule is represented by d/dx (8) = 0?
constant rule
sum rule
chain rule
constant multiple rule
23
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)]
24
Find y' for y=sin
-1
(1-t)
-1 / sqrt(2t-t2)
1 / (2t-t2)
1
y' does not exist
25
Which of the following is not true about the derivatives of trig functions?
d/dx csc(x) = csc(x)cot(x)
d/dx tan(x) = sec2(x)
d/dx sin(x) = cos(x)
d/dx cot(x) = -csc2(x)
26
All of the following are proper notations for the derivative f(x), f(x) is replaceable by y
y'
df/dx
dy/dx
d/dx
27
If x(t)=t
2
+t and y(t)=sin(t), find dy/dx as a function of t.
cos(t) / (2t +1)
sin(t) / (2t +1)
cos(t)*(2t +1)
cos(t) / 2t
28
If a particle's position is represented by s(t)=(t
2
-4t+3) / (t+1), find the velocity at t=2
9
1/3
1/9
2/9
29
Find dy/dx for y = (x) / (1 + cos(x))
[1-cos(x)+3xsin(x)] / [1+2cos(x)+cos2(x)]
[1+cos(x)+xsin(x)] / [1+2cos(x)+cos2(x)]
[1+cos(x)+xsin(x)]
[1] / [1+2cos(x)+cos2(x)]
30
Which of the following is true about the domains of a function and its derivative f'(x)?
domain f(x) is less than or equal to the domain f'(x)
domain f(x) is greater than or equal to the domain f'(x)
