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Derivatives Flashcards | StudBud
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Derivatives
Derivatives
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This is a chapter review game for derivatives in a Calculus BC class.
Flashcards
18 cards
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Practice quiz
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Questions
18
Answers
1
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
2
Find f'(x) for f(x) = (x
2
+1)(x
3
+3)
5x4+6x
5x-3x2+6
5x4+3x2+6x
5x4+3x
3
Which of the following is not a derivative rule?
second derivative rule
difference rule
sum rule
constant multiple rule
4
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 ex = ex
d/dx ax = axln(a)
5
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)+xsin(x)]
[1-cos(x)+3xsin(x)] / [1+2cos(x)+cos2(x)]
6
If f has a derivative at x=a, then f is continuous at x=a.
True
False
7
Find y'', the second derivative, for y = x
3
-5x
2
+2
3x2-10x
does not exist
6x-10
6
8
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 = 1/2(x - 1)
y - 2 = 1/3(x - 2)
y = 1/2(x - 1)
9
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)
10
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)
11
Which of the following represents the power rule?
d/dx(xn) = nxn-1
d/dx(xn) = (n) / (xn)
d/dx(xn) = (n-1)xn
d/dx(xn) = nxn+1
12
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)
13
If a particle's position is represented by s(t)=t
2
-4t+3, find the acceleration at t=3
2
6
1/2
does not exist
14
All of the following are proper notations for the derivative f(x), f(x) is replaceable by y
df/dx
y'
d/dx
dy/dx
15
What rule is represented by d/dx (8) = 0?
sum rule
constant rule
chain rule
constant multiple rule
16
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
17
For the graph below, does f'(0) exist?
yes
no
18
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)]
