00:01
Okay, so for this problem, we have the function w of x, y, and z, and that's going to equal x, y, cosine, z.
00:12
We are also given that we have x equals t, y equals t squared, and z equals arc sign of t.
00:25
Okay, so what we are asked to do is go through and find, is to go ahead and solve the problem by finding, using the change, line rule to find the derivative.
00:37
So what we want to do is we're going to have to do a couple of things first, but i'm going to scoot down because we want to do it right out our chain rule for this.
00:43
So we're finding dwdt.
00:49
So it's going to be dw over dx and then dx over dt.
00:55
And if you notice the dx would cancel if we were multiplying these.
00:59
And then dw over dy, dy over dt.
01:06
And then dw over dz, and then dz over dt.
01:13
So we're going to need quite a few derivatives.
01:15
So what i want to do is i want to go back up to the top, and let's go ahead and do those first.
01:22
So if i'm looking at this, i've got dw over dx.
01:26
So if i look at this and i'm deriving this, that means in terms of x, that means y and our z are going to be constants, or are y and cosine z.
01:34
So since x is singular, it means there's no, it's just one of an exponent, it's going to be y cosine z...