stud
bud
Sign up
Log in
Home
Library
Explore
SAT
More
Calculus Basic Derivatives Flashcards | StudBud
Explore
/
Calculus Basic Derivatives
Calculus Basic Derivatives
30 terms
·
StudBud Administration
·
12 plays
Calculus Final First Half of Derivatives
Flashcards
30 cards
F
Practice quiz
P
Host live
L
Questions
30
Answers
1
If f(x) has a max or min, what is f'(x) at that point?
DNE
none
0
Both 0 and DNE
2
Derive ln(e
x
+e
-x
)
(ex+e-x)/(ex+e-x)
(ex-e-x)/(ex+e-x)
(ex-e-x)/(ex-e-x)
(ex+e-x)/(ex-e-x)
3
Solve by implicit differentiation: xlny = 10
4
(-lny *y)/x
(lnx*x)/y
(lnx *y)/y
(lny*y)/x
4
Derive ln(lnx
2
)
1/xlnx2
2/xlnx
1/xlnx
2/lnx2
5
Solve the given problem
a = -2.5 b = 1.5
a= 1.5 b= -2.5
a= 2.5 b = 1.5
a = -1.5 b= 2.5
6
What is the derivative of e
-x
?
-e-x
ex
e-x
-ex
7
Solve by implicit differentiation: y
3
+y
2
-5y-x
2
=-4
-(3y2+2y-5)/(2x)
(3y2+2y-5)/(2x)
-(2x)/(3y2+2y-5)
(2x)/(3y2+2y-5)
8
True or false: if a function is differentiable, then it must be continuous
False
True
9
Solve by implicit differentiation: x
2
+y
2
=25
x/y
-y/x
-x/y
y/x
10
If f '(x) is negative, what is the graph of f(x) doing?
Decreasing
It is below the x-axis
Increasing
It is above the x-axis
11
What is the acceleration of the equation 2x
5
+x
3
+9?
x3+x2
2x6+x4+9x
10x4+3x2
40x3+6x
12
What is the derivative of 5
(x-2)
?
(x-2)5(x-1)
lnx * 5(x-2)
(x-2)5(x-3)
ln5 * 5(x-2)
13
If position is represented by f(x)= csc(x), what function represents velocity?
sec2x
csc(x)cot(x)
sec(x)tan(x)
-csc(x)cot(x)
14
What is the definition of a derivative at a point?
the y-intercept
the x-intercept
the limit from -∞ to ∞
slope of the tangent line
15
What is the derivative of sin
3
4t?
(-12sin24t)(cos4t)
(12sin24t)(cos4t)
-12cos24t
12sin24t
16
What is the derivative of a constant?
It does not exist
x
0
the constant
17
What is the Quotient Rule?
f'/g' = (d/dx)(f/g)
f'/g' = (((gf')+(fg"))/g2
f'/g' = ((g'f)-(f'g))/g2
f'/g' = ((gf')-(fg'))/g2
18
Where are there no derivatives?
A sharp turn
All of the above
Vertical tangent
A point of discontinuity
19
What is the derivative of (9x
3
-7x
2
)
-8
?
(9x3-7x2)-7
-8(27x2-14x)-9
(27x2-14x)-8
-8(9x3-7x2)-9•(27x2-14x)
20
What is the derivative of x/(x-2)?
0
1/(x-2)
DNE
(X-2)-(x)/(x-2)2
21
If f '(x) is sec(x)tan(x), what could the original function be?
sin(x) +7
tan(x) +7
csc(x) +7
sec(x) +7
22
Which is the derivative graph for the graph of f(x)?
A
D
C
B
23
True or False?
d/dx
(f•g) = f'•g'
False
True
24
What is the derivative of sin(x)/e
3x
?
e-3x(3cos(x)-sin(x))
e-3x(cos(x)-3sin(x))
-e-3x(cos(x)-3sin(x))
-e-3x(3sin(x))
25
If f(x) is the original equation, what is the derivative?
B
C
D
A
26
What is the rule that is used to find the derivative of (tan)
12
?
Newton's 12th law
Product rule
Quotient rule
Chain rule
27
Given that g(5)=-3, g'(5)=6, h(5)=3, and h'(5)=-2, find f '(5) for f(x)=g(x)h(x)
6
22
24
18
28
If the graph of f(x) is increasing, what is the graph of f '(x)?
The derivative graph does not exist
Positive
Oscilating
Negative
29
What is the general definition of a derivative?
the slope at the point
lim(Δx→0) (f(x+Δh)-f(x)) / Δx
the limit from -∞ to ∞
30
What is the derivative of cos
15
(x
2
-9x)?
0
15(cos(x2-9x))14 *(-sin(x2-9x)*(2x-9))
-15sin(x2-9x)*(2x-9)
15(cos(2x-9))14
