00:01
All right, let's jump right into problem four in chapter 15, six, and four.
00:05
All right, so we're asked to solve for, or not asked to solve.
00:10
We are asked to explain how we solve for the partial derivative of z divided by t, this guy.
00:18
All right, so let's draw a tree diagram to start.
00:21
So we have our z at the top, and then that goes down to x, which is then branches off in two directions.
00:31
So we've got s and t.
00:37
In the other side, we've got y.
00:41
I can drop better y than that.
00:44
And that branch also branches off into s and t.
00:51
Okay, so we can start writing this, and we see that we get a partial derivative from here to here.
01:02
So we'd have a partial derivative of z with respect to x, multiplied by.
01:19
And here you're going to think, oh, since we've been doing it before, it's just a derivative.
01:23
Well, no, because we've got to write a partial derivative here.
01:26
I'll explain why in a second...