stud
bud
Sign up
Log in
Home
Library
Explore
SAT
More
Chapter 3 Review: Derivatives Flashcards | StudBud
Explore
/
Chapter 3 Review: Derivatives
Chapter 3 Review: Derivatives
31 terms
·
StudBud Administration
·
222 plays
This is a chapter review game for derivatives in a Calculus BC class.
Flashcards
31 cards
F
Practice quiz
P
Host live
L
Questions
31
Answers
1
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
cos(t)*(2t +1)
sin(t) / (2t +1)
2
Use the limit of the difference quotient to determine the derivative of f(x)=x
3
3x3
3x2+3h
3x2
x3+x+h
3
Which of the following is not a derivative rule?
difference rule
constant multiple rule
sum rule
second derivative rule
4
Which of the following is not true about the derivatives of exponential and log functions?
d/dx ln(x) = 1/x
d/dx ex = ex
d/dx ax = axln(a)
d/dx logax = ln(a) / x
5
Using left and right handed derivatives, does the derivative at x=0 exist for the function...
yes, y'(0) = 0
yes, y'(0) = 2
yes, because the function is defined at x=0
No, f'(0) does not exist
6
Find dy/dx for xsin(2y) = ycos(2x)
1
dy/dx does not exist
[-2ysin(2x)-sin(2y)]*[cos(2x)]
[-2ysin(2x)-sin(2y)]/[2xcos(2y)-cos(2x)]
7
What rule is represented by d/dx (8) = 0?
constant multiple rule
constant rule
sum rule
chain rule
8
Find y' for y=sin
-1
(1-t)
1
1 / (2t-t2)
y' does not exist
-1 / sqrt(2t-t2)
9
Which of the following is not true about the derivatives of inverse trig functions?
d/dx arccos(x) = -1 / [sqrt(1-x2)]
d/dx arcsec(x) = 1 / [ |x|(x2-1) ]
d/dx arctan(x) = 1 / (1+x2)
d/dx arcsin(x) = 1 / [sqrt(1-x2)]
10
Who is responsible for discovering Calculus?
Issac Newton and Gottfried Wilhelm von Leibniz
Mrs. Mascotti
Issac Newton
Gottfried Wilhelm von Leibniz
11
If a particle's position is represented by s(t)=(t
2
-4t+3) / (t+1), find the velocity at t=2
1/9
1/3
9
2/9
12
Find dr/dx for r = tan(2-x)
-sec2(2-x)
sec2(2-x)*(2-x)
-tan(2-x)
sec2(2-x)
13
If f has a derivative at x=a, then f is continuous at x=a.
True
False
14
Find y'', the second derivative, for y = x
3
-5x
2
+2
6
3x2-10x
6x-10
does not exist
15
Find y' for y=sin
3
(x)tan(4x)
sin2(x) + 4sin(x) - 3cos(x)
sin2(x) [3cos(x)tan(4x) + 4sin(x)sec2(4x)]
4sin3(x)sec2(4x)
1
16
Using implicit differentiation, find dy/dx for x
2
- xy + x
2
= 7
none of the above
dy/dx = 1
dy/dx = (y-2x) / (2y-x)
dy/dx = (y^2) / (-2x + y)
17
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)
18
The function y = (x)
2/3
fails to be differentiable at x=0, what type of problem is at x=0?
corner
discontinuity
cusp
vertical tangent
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
If y=ln(x
2
), find y'.
2
2x2
2/x2
2/x
21
Find y' for y=x
2
e
x
- xe
2x
3ex(x2+2x)-7e2x(2x+1)
ex(x2+2x)-e2x(2x+1)
1
ex(x2+2x)
22
Find f'(x) for f(x) = (x
2
+1)(x
3
+3)
5x4+3x2+6x
5x4+6x
5x-3x2+6
5x4+3x
23
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)
24
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)]
25
For the graph below, does f'(0) exist?
no
yes
26
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 tan(x) = sec2(x)
d/dx csc(x) = csc(x)cot(x)
27
All of the following are proper notations for the derivative f(x), f(x) is replaceable by y
y'
dy/dx
df/dx
d/dx
28
Who is the coolest guy in the room? (hint below)
Adam Coppock
All of the Above
Mr. Coppock
Adam
29
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
limit as h approaches 0 of [f(x+h) + f(x)] / x
limit as h approaches 0 of [f(x+h) - f(x)] / h
All of the above
30
If a particle's position is represented by s(t)=t
2
-4t+3, find the acceleration at t=3
2
does not exist
1/2
6
31
Which of the following is not true about the derivatives of trig functions?
d/dx cos(x) = -sin(x)
d/dx tan(x) = sec2(x)
d/dx sec(x) = sec(x)tan(x)
d/dx sin(x) = -cos(x)
