00:01
Okay, so for this problem, we are given the equation z equals e to the 1 minus xy power.
00:08
We are given that x equals t to the one third power and that y equals t to the third power.
00:16
Okay.
00:18
And so what we're asked to find, and i'm going to do this in a different color, is dz over dt.
00:27
And since the equation of z doesn't have a t variable, we're going to use the chain roll.
00:32
So dz over dx, dx over d t, plus d z over d y, d y over d t.
00:44
Okay, so now let's go back up to the top and actually go ahead and find these values.
00:47
All we have to do is plug them in.
00:50
So dz over dx.
00:53
So i'm going to have e to the 1 minus xy power.
00:58
Then if we take the derivative of 1, that's 0, so we can ignore it.
01:02
And then the derivative of xy or negative xy in terms of is going to be negative y.
01:11
And then i'm going to find d z over d y.
01:16
So if i do the same thing, so it's e to the one minus xy power, this one's going to be negative x.
01:25
And then d x over d t is going to be one third t to the negative two thirds.
01:36
And d y over d t is going to be three t squared...