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Derivatives
Derivatives
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A Calculus Review of derivatives
Flashcards
23 cards
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Practice quiz
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Questions
23
Answers
1
What is the equation for the derivative of tan
-1
x ?
-U'/√(1-U2)
U'/√(1-x2)
-U'/√(1-x2)
U'/(1+U2)
2
What is a critical point?
nothing
where the derivative is zero or the derivative DNE
the slope of the entire line
a point that has a slope of 1
3
What do you find when you find the second derivative?
concavity
nothing
slope of the tangent line
4
What is the equation for the derivative of cot
-1
x ?
-U'/√(1-U2)
U'/|U|√(U2-1)
U/(1+U2)
-U'/(1+U2)
5
dy/dx (x - 1)(x
2
+ 3)
3x2 + 2x + 3.
-3x2 - 2x + 3.
3x2 - 2x + 3.
3x2 - 2x - 3.
6
What is the equation for the derivative of cos
-1
x ?
-U'/√(1-x2)
U'/√(1-x2)
-U'/√(1-U2)
1/(1+x2)
7
What is the equation for the derivative of sin
-1
x ?
U/√(1-U2)
U'/√(1-U2)
U'/(1-U2)
U'/√(U2-1)
8
dy/dx (x + 2)
2
- 5x
3
15x2 - 2x - 4
-15x2 - 2x - 4
15x2 + 2x + 4
-15x2 + 2x + 4
9
What do you find when you find the First derivative?
slope of the tangent line
nothing
sinx
Concavity
10
How do you find points of inflection?
Find the First Derivative of the function
Find the third Derivative of the function
Find the Second Derivative of the function
Multiply by the derivative
11
dy/dx 5x
3
- √2x
2
+ 6x
15x2 - 2√2x - 6
15x2 - 2√2x + 6
15x3 - 2√2x + 6.
5x3 - √2x2 + 6x
12
What is the equation for the derivative of csc
-1
x ?
U'/|U|√(U2-1)
U/(1+U2)
-U'/|U|√(U2-1)
-U'/(1+U2)
13
Are critical points the same as inflection points?
Yes
Sometimes
No
14
dy
2
/
dx
2
2x
3
+3x-6
6
6x2+3
12x
2x3+3x-6x
15
What is the derivative of sinx?
cosx
-sinx
secxtanx
-cosx
16
What is the derivative of cosx?
-sinx
sinx
cosx
-cosx
17
What is the derivative of cscx?
cscxcotx
tanx
-cscxcotx
csc2x
18
What is the derivative of cotx?
cscxcotx
csc2x
-csc2x
-cscxcotx
19
What is the derivative of tanx?
secxtanx
-csc2x
sinx/cosx
sec2x
20
How do you find a critical point?
Set derivative equal to zero and solve for x
Set second derivative equal to one and solve for x
Set second derivative equal to zero and solve for x
Set equation equal to zero and solve for x
21
What is the derivative of secx?
secxtanx
cscx
sec2x
-secxtanx
22
What is an inflection point?
nothing
Where concavity changes
where the slope changes
slope = 0
23
What is the equation for the derivative of sec
-1
x ?
-U'/(1+U2)
-U'/|U|√(U2-1)
U'/|U|√(U2-1)
U/(1+U2)
