role
stringclasses
2 values
content
stringlengths
0
2.1k
session_id
int64
10
21.7k
sequence_id
int64
0
2.38k
annotations
listlengths
0
8
volunteer
excellent
13,524
55
[]
volunteer
now how can we change 4d to d?
13,524
56
[]
student
Last thing to do would be to divide everything by 4 correct?
13,524
57
[]
volunteer
yes
13,524
58
[]
volunteer
Now a comment
13,524
59
[]
volunteer
since 4 is positive that is fine
13,524
60
[]
volunteer
IF it were negative it would reverse the inequality DO u know that?
13,524
61
[]
student
Yes
13,524
62
[]
volunteer
wait
13,524
63
[]
volunteer
it does not reverse
13,524
64
[]
volunteer
since 4 > 0
13,524
65
[]
student
What do you mean?
13,524
66
[]
volunteer
I will write
13,524
67
[]
volunteer
my writing is ot so good but do you see what I mean?
13,524
68
[]
student
Yes but shouldn’t the sign change since we have divided by a negative?
13,524
69
[]
volunteer
Yes but we divided all by 4 ad 4 is *not* meg
13,524
70
[]
volunteer
neg*
13,524
71
[]
volunteer
see what I wrote
13,524
72
[]
volunteer
My commenbt was correct but I htink it was confusing
13,524
73
[]
student
Alright that makes sense
13,524
74
[]
volunteer
OK so I think we have the answer
13,524
75
[]
volunteer
Now can you grpah it?
13,524
76
[]
student
Like that?
13,524
77
[]
volunteer
wait I will scroll
13,524
78
[]
volunteer
yes
13,524
79
[]
volunteer
and what kind of dots at each end open or closed?
13,524
80
[]
student
Closed
13,524
81
[]
volunteer
I agree
13,524
82
[]
volunteer
Did you see the cnfetti?
13,524
83
[]
student
Yes!
13,524
84
[]
student
Thank youuu
13,524
85
[]
volunteer
good
13,524
86
[]
volunteer
OK might you have a TI-84 cal;ciultor?
13,524
87
[]
student
Unfortunately not
13,524
88
[]
volunteer
OK no problem
13,524
89
[]
volunteer
I think they can grpah inequal
13,524
90
[]
volunteer
But thii fine
13,524
91
[]
volunteer
you did vey well
13,524
92
[]
volunteer
very*
13,524
93
[]
volunteer
sorry I confsuded you about the sign
13,524
94
[]
student
No problem you explained it very well!
13,524
95
[]
volunteer
Good thanks
13,524
96
[]
student
Have a lovely day!
13,524
97
[]
volunteer
You too BYE BYE
13,524
98
[]
student
:]
13,524
99
[]
volunteer
Hi Liam
13,550
0
[ { "pii_type": "PERSON", "surrogate": "Liam", "start": 3, "end": 7 } ]
student
Hello could you help me understand inverse trig functions
13,550
1
[]
student
like with derivatives and implicit differentiation
13,550
2
[]
volunteer
OK. Do you have a specific question or problem you'd like to work on?
13,550
3
[]
student
I guess just understanding in general but let me pull one up
13,550
4
[]
student
have you taken calculus?
13,550
5
[]
volunteer
Yes.
13,550
6
[]
student
Okay, im in BC not AB but that was the only option
13,550
7
[]
volunteer
No problem.
13,550
8
[]
volunteer
The problem shows how to find the derivative of the "inverse tangent" function.
13,550
9
[]
student
i know the derivative of the inverse tan and the inverses of trig functions and are familiar with that
13,550
10
[]
student
okay
13,550
11
[]
volunteer
So you need help with "implicit differentiation" ?
13,550
12
[]
student
no just this concept like why change sec squared y to Noah squared Tampa and how then did it transform to x
13,550
13
[ { "pii_type": "PERSON", "surrogate": "Noah", "start": 54, "end": 58 }, { "pii_type": "LOCATION", "surrogate": "Tampa", "start": 67, "end": 72 } ]
student
why does tan y =x
13,550
14
[]
volunteer
Let's start with sec^2(y) = tan^2(y)+1. It's a trigonometric identity. I can explain if you wish.
13,550
15
[]
student
i am familar with the concept
13,550
16
[]
student
i dont need help with that
13,550
17
[]
volunteer
So you need help with tan y = x?
13,550
18
[]
student
i guess yes
13,550
19
[]
student
like i understand when im looking at it but when im doing an actual problem im scared im going ot mess up
13,550
20
[]
student
let me replace it with an actual problem
13,550
21
[]
volunteer
OK.
13,550
22
[]
student
so finding the derivative
13,550
23
[]
volunteer
I think you mean something a bit different. I'll write.
13,550
24
[]
student
okay
13,550
25
[]
volunteer
Is this what you meant?
13,550
26
[]
student
yes apolgies
13,550
27
[]
student
is all i do is plug in x/2 into the derivative of inverse sin
13,550
28
[]
volunteer
Yes. You also need the chain rule.
13,550
29
[]
volunteer
I can show you if you wish.
13,550
30
[]
student
i know the chain rule
13,550
31
[]
student
is it purely just 1/ the square root of (x/2)^2-1) switch the 1 and x/2
13,550
32
[]
volunteer
It would be: 1/√(1-(x/2)^2)*(1/2).
13,550
33
[]
student
adn the 1/2 is from the chain rule?
13,550
34
[]
volunteer
Correct.
13,550
35
[]
student
okay i think i get that it seems simple enough
13,550
36
[]
volunteer
Awesome!
13,550
37
[]
student
could i ask one more questions?
13,550
38
[]
volunteer
Sure.
13,550
39
[]
volunteer
You'll need to use implicit differentiation to solve this problem.
13,550
40
[]
student
okay
13,550
41
[]
student
would the first step be e to the y - e to the y^2 * 2y*dy/dx=1-3x^2
13,550
42
[]
volunteer
Yes. Then solve the equation for dy/dx = ?
13,550
43
[]
volunteer
You forget one thing.
13,550
44
[]
volunteer
*forgot
13,550
45
[]
volunteer
The first term would be (e^y)*dy/dx.
13,550
46
[]
student
oh oh is it e*dy/dx - 2ye to the dy/dx
13,550
47
[]
student
ah i see
13,550
48
[]
student
and -2yeto the y^2 *dy/dx is because of the chain rule?
13,550
49
[]
volunteer
Yes.
13,550
50
[]
volunteer
I wrote above your uploaded page.
13,550
51
[]
student
okay thanks!
13,550
52
[]
student
so whenever you have e the power (in this case y ^2) will be what we are using for chain rule?
13,550
53
[]
student
like it would be f of the deravitive of f(g(x))*g(x)
13,550
54
[]