00:01
All right, so we want to find the derivative of this function, the determinant of the matrix that has an x hanging out here.
00:06
Seems a little bit tricky, and i'm not going to lie, it is a little bit tricky, but what we can do, what we want to do is expand this out, right? and we're going to do that with cofactor expansion first along the top row here.
00:22
So f of x is equal to 1 times the determinant of this matrix here.
00:31
I'm going to call just a.
00:34
Let's make my green pen a little bit wider here.
00:39
1 times the determinant of a minus 9 times the determinant of this other matrix here.
00:52
But actually what you'll, what we're going to see here is that it's just a ton of constants, right? it's 1 times the determinant of something that doesn't depend on x, then we get 9 times the determinant of something that doesn't depend on x, plus 9 times the determinant of something that doesn't depend on x...