stud
bud
Sign up
Log in
Home
Library
Explore
SAT
More
derivatives calculus project Flashcards | StudBud
Explore
/
derivatives calculus project
derivatives calculus project
40 terms
·
StudBud Administration
calculus game project by: rebecca lopez & elliot sabatini
Flashcards
40 cards
F
Practice quiz
P
Host live
L
Questions
40
Answers
1
If y = 3x^2 + 2, what is dy/dx?
3x
3
2x
6x
2
If g(x) = cos(3x), what is g'(x)?
3cos(3x)
-3cos(3x)
-3sin(3x)
3sin(3x)
3
If h(x) = cos(x), what is h''(x)?
sin(x)
-sin(x)
cos(x)
-cos(x)
4
The slope of the tangent line to a curve at a point is given by:
The integral of the function
The derivative of the function
The limit of the function
The sum of the function
5
What is the derivative of e^(2x) with respect to x?
2e^(2x)
4e^(2x)
2xe^(2x)
e^(2x)
6
What is the derivative of a constant function?
0
1
the constant
undefined
7
What is the derivative of cot(x)?
cosec^2(x)
-cosec(x)cot(x)
-cosec^2(x)
cosec(x)cot(x)
8
What is the derivative of x^2 with respect to x?
2x
2
1/x
x
9
What is the second derivative of x^3?
0
3
6x
3x^2
10
What is the derivative of ln(x)?
1/x
In(x)
x
-1/x
11
If f(x) = √x, what is f'(x)?
2√x
1/(√x)
1/(2x)
1/(2√x)
12
The critical points of a function occur where:
The function is undefined or zero
The integral is maximal
The function is differentiable
The function is continuous
13
The chain rule is used to find the derivative of:
Composite functions
Quotient of functions
Sum of functions
Product of functions
14
The product rule is used to find the derivative of:
Product of functions
Quotient of functions
15
If h(x) = sin^2(x), what is h'(x)?
cos(2x)
sin(2x)
2sin(x)cos(x)
2cos(x)
16
The inverse function rule is used to find the derivative of:
Sum of functions
Inverse functions
Composite functions
Product of functions
17
The power rule is used to find the derivative of:
Sum of functions
Quotient of functions
Functions in the form ax^n
Product of functions
18
What is the derivative of sec(x)?
sec(x)tan(x)
-sec(x)tan(x)
-cosec(x)cot(x)
cosec(x)cot(x)
19
If f(x) = ln(4x), what is f'(x)?
4/(4x)
1/(4x)
1/x
4/x
20
The logarithmic differentiation technique involves:
Factoring the expression
taking the logarithm of both sides
multiplying by the exponent
Differentiating directly
21
If g(x) = ln(2x), what is g'(x)?
1/(2x)
1/x
in(2x)
2/x
22
If f(x) = e^(3x) - 2x^2, what is f'(x)?
3e^(3x) - 4x^2
9e^(3x) - 4x^2
9e^(3x) - 4x
3e^(3x) - 4x
23
If f(x) = 1/x, what is f''(x)?
2/x^3
-2/x^3
-1/x^3
1/x^3
24
The quotient rule is used to find the derivative of:
Sum of functions
Composite functions
Quotient of functions
Product of functions
25
If g(x) = e^x - ln(x), what is g'(x)?
e^x - ln(x)
e^x - 1/x
e^x + 1/x
e^x + ln(x)
26
What is the derivative of arctan(x)?
1/(1-x^2)
1/(1+x^2)
x/(1+x^2)
x/(1-x^2)
27
If p(x) = 2x^3 - 5x^2 + 3x + 1, what is p'(x)?
6x^2 - 10x - 3
6x^2 - 5x - 3
6x^2 - 10x + 3
6x^2 - 5x + 3
28
If h(x) = 5/x, what is h'(x)?
1/x^2
5/x^2
-1/x^2
-5/x^2
29
What is the derivative of tan(x)
sec^2(x)
cos(x)
cot(x)
sin(x)
30
If h(x) = ln(x^2), what is h'(x)?
2x
1/x^2
2ln(x)
2/x
31
If f(x) = e^(2x) - 4x, what is f'(x)?
e^(2x) - 4x
2e^(2x) - 4x
e^(2x) - 4
2e^(2x) - 4
32
If y = 4x^2 + 3x - 2, what is dy/dx?
8x + 3
8x^2 - 3
8x^2 + 3
8x - 3
33
If f(x) = 3x^4, what is f'(x)?
9x^3
4x^3
12x^3
3x^3
34
The arc length formula involves the use of:
The derivative of a function
The limit of a sequence
The sum of a series
The integral of a function
35
If f(x) = e^(3x), what is f''(x)?
27e^(3x)
9e^(3x)
6e^(3x)
3e^(3x)
36
What is the derivative of sin(x)?
cos(x)
-cos(x)
sin(x)
-sin(x)
37
The sum rule is used to find the derivative of:
product of functions
sum of functions
Quotient of functions
composite functions
38
If f(x) = x^3 - 2x^2 + 4x - 1, what is the critical point(s) of f(x)?
x = 1
x = 0
x = 2
x = 3
39
If g(x) = e^x, what is g'(x)
1
e^x + 1
e^x
40
If f(x) = 3x^2 + 2x + 1, what is f''(x)?
6x + 3
2
6
6x + 2
