00:01
Okay, so let's evaluate the curl of our vector field f.
00:06
Okay, this one is going to be the determinant of the matrix i, j, k here, partial derivative with respect to x, partial derivative with respect to y, partial derivative with respect to y, partial derivative with respect to z.
00:22
And now we are going to have negative 9y here.
00:26
Okay, then we are going to have 6y squared.
00:31
Okay, so 6y squared minus 9 z squared minus 9 x squared minus 9 x minus 9 z so minus 9 x minus 9 z okay and finally the last one is negative 18 y z negative 18 y z negative 19 y z negative 9 y okay so now we are going to use the laplace expansion with respect to the first row okay so with respect to the first row the first coordinate is going to be what negative 18 z negative 18 z minus the partial derivative of this one with respect to z okay which is 18 z okay, the second coordinate is going to be, okay, negative one here, so just the negative sign.
01:47
Okay, and now we're going to have the partial derivative of this one with respect to x, which is zero, minus the partial derivative with respect to this one, which is again zero.
02:00
So, okay, i'm just going to write zero here.
02:05
And finally, for the third one, the partial derivative of this...