WEBVTT
1
00:00:01.340 --> 00:00:06.209 A:middle L:90%
eso I would rewrite this problem as X tangent of
2
00:00:06.219 --> 00:00:09.519 A:middle L:90%
X to the Nega first power. And that is
3
00:00:09.519 --> 00:00:13.240 A:middle L:90%
one over X. Um, that just might help
4
00:00:13.240 --> 00:00:15.369 A:middle L:90%
you. When you get to the chain rule,
5
00:00:15.380 --> 00:00:19.160 A:middle L:90%
you have your inter function and your outer function and
6
00:00:19.160 --> 00:00:21.589 A:middle L:90%
right here is telling you to do the product rule
7
00:00:22.579 --> 00:00:26.820 A:middle L:90%
. So the first derivative you take the drift of
8
00:00:26.820 --> 00:00:28.550 A:middle L:90%
of X, which is one you know how to
9
00:00:28.550 --> 00:00:31.350 A:middle L:90%
write that you leave the tangent of one over x
10
00:00:31.350 --> 00:00:34.829 A:middle L:90%
alone. Plus now you leave X alone, the
11
00:00:34.829 --> 00:00:41.509 A:middle L:90%
derivative of tangent seeking squared and you leave the one
12
00:00:41.509 --> 00:00:43.740 A:middle L:90%
over X alone or extra the negative one. And
13
00:00:43.740 --> 00:00:46.270 A:middle L:90%
then you have to multiply by the drift of of
14
00:00:46.270 --> 00:00:50.100 A:middle L:90%
this, which is negative one ext of a negative
15
00:00:50.100 --> 00:00:53.259 A:middle L:90%
second power. Now, before I do anything from
16
00:00:53.259 --> 00:00:57.399 A:middle L:90%
here, I would just simplified this a little bit
17
00:00:58.960 --> 00:01:08.689 A:middle L:90%
because if you add your exponents, um, you
18
00:01:08.689 --> 00:01:11.349 A:middle L:90%
end up with X and the denominator, and I
19
00:01:11.349 --> 00:01:17.140 A:middle L:90%
should have rewrote that as minus because you have a
20
00:01:17.140 --> 00:01:21.480 A:middle L:90%
negative one there. Um, yeah, one of
21
00:01:21.480 --> 00:01:23.849 A:middle L:90%
those excess will cancel. So now from here,
22
00:01:23.299 --> 00:01:26.420 A:middle L:90%
I can't find the second derivative because that's what the
23
00:01:26.420 --> 00:01:30.310 A:middle L:90%
direction I want you to do. And this is
24
00:01:30.310 --> 00:01:33.939 A:middle L:90%
your chain rule, just like what we did earlier
25
00:01:34.459 --> 00:01:36.349 A:middle L:90%
. Except you don't have the X in front.
26
00:01:36.930 --> 00:01:41.790 A:middle L:90%
Um, so the drift of tanginess seeking squared of
27
00:01:41.790 --> 00:01:45.329 A:middle L:90%
one over X. Um and you already see I
28
00:01:45.329 --> 00:01:47.310 A:middle L:90%
wrote the negative here because this is the same thing
29
00:01:47.310 --> 00:01:49.459 A:middle L:90%
Is before accident a get first. So negative one
30
00:01:49.469 --> 00:01:56.150 A:middle L:90%
exiting of second over X squared. So now this
31
00:01:56.150 --> 00:01:59.370 A:middle L:90%
is a different kind of rule. Um, because
32
00:01:59.370 --> 00:02:01.590 A:middle L:90%
it's a quotient rule and the drift of of the
33
00:02:01.590 --> 00:02:05.950 A:middle L:90%
top is a chain rule for sure. Where you
34
00:02:05.950 --> 00:02:08.409 A:middle L:90%
want to bring the two in front, You leave
35
00:02:08.409 --> 00:02:12.009 A:middle L:90%
seeking of one over x alone. But then the
36
00:02:12.009 --> 00:02:15.370 A:middle L:90%
derivative of seeking is seeking tangent. I mean,
37
00:02:15.370 --> 00:02:17.949 A:middle L:90%
right Siegen squares on to write that again, tangent
38
00:02:20.689 --> 00:02:23.750 A:middle L:90%
of one over X and then the derivative of one
39
00:02:23.750 --> 00:02:25.789 A:middle L:90%
of her ex. Just like what I had before
40
00:02:25.789 --> 00:02:29.250 A:middle L:90%
is that negative? One Excellent. And of second
41
00:02:29.250 --> 00:02:34.569 A:middle L:90%
power times have on next hour. And then you
42
00:02:34.569 --> 00:02:38.139 A:middle L:90%
need to leave the denominator alone, which is times
43
00:02:38.139 --> 00:02:44.860 A:middle L:90%
X minus the drift of of the bottom which is
44
00:02:44.860 --> 00:02:46.300 A:middle L:90%
just one. You leave the top alone. You
45
00:02:46.300 --> 00:02:52.110 A:middle L:90%
can squared of one over X all over the denominator
46
00:02:52.110 --> 00:02:54.159 A:middle L:90%
squared. Now I think I'm past my time of
47
00:02:54.430 --> 00:02:58.009 A:middle L:90%
simplification, but there's a lot of things that you
48
00:02:58.009 --> 00:03:00.699 A:middle L:90%
can simplify. I can put these fractions together because
49
00:03:00.699 --> 00:03:02.789 A:middle L:90%
they're both over X squared. This piece might put
50
00:03:02.789 --> 00:03:06.979 A:middle L:90%
a hiccup in that you could factor things out.
51
00:03:06.979 --> 00:03:07.669 A:middle L:90%
There's so much more you can do. I don't
52
00:03:07.669 --> 00:03:09.590 A:middle L:90%
know where to stop, So I'm gonna stop right
53
00:03:09.590 --> A:middle L:90%
there.