00:03
Okay, f is a function of u, v, and w, and each of u, v, and w are functions of x, y, and z.
00:13
Okay, so if we want to find dfdx, it's going to be df, d .u, d -x, plus d -f -d -v, d -v -d -x, plus d -f -d -z, or d -f -d -w, d -d -x.
00:53
Okay, that's d -f -dx.
00:55
And then similar, each one of the other function, or each other, of the other derivative, will be just like that.
01:03
So d, f, d, d, y will be d -f -d -u -d -y plus d -v -d -y, d -d -y, plus d -f -d -w, d -d -x.
01:26
And then d -f -d -z is d -f -d -d -u -d -z plus d -f -d -d -v -d -d -d -z plus d -f -d -d -d -w, dw, dw, dz.
01:49
Why is that one having x at the end? i don't know.
01:52
That should be d .y.
01:56
All right, so we don't really know what f is.
02:00
We just know it's a function and it's differentiable.
02:03
So somehow the u's and v's and w's must turn into something interesting.
02:11
Ok, so here we go.
02:12
Df, dx.
02:13
That's df, d, d, u times du, dx...