00:01
Alright, so we want to find the derivative dw with respect to dt.
00:04
So the total derivative dw is going to be dw dx times dx dt plus dw dy times dy dt plus dw dz times dz dt.
00:27
Okay, so dw with respect to dx is going to be 10 times x, just bringing down the power, and then the rest of it is treated as constants.
00:41
And then dx dt, well, x is t squared, so dx dt is going to be 2t.
00:48
And then we have plus dw dy, so it's going to be, we move the 3 out in front, so that's 15x squared y squared z to the fourth.
00:59
Dy dt is going to be 3t squared.
01:05
And then plus dw dz, 5 times 4 is 20x squared y cubed z to the third power.
01:14
And then we have 5t to the fourth for the dz dt...