00:01
All right, we've been asked to test if this vector field is conservative.
00:05
A quick way to test if a vector, oh, quick, whatever.
00:09
A good way to test whether a vector field is conservative is, does it pass the cross -partials test? and that's basically saying, we'll call this f sub x, we'll call this f sub y, and we'll call this, oh, sorry, this is k hat, we'll call this f sub z and if all three of these that i'm about to write are satisfied then it's conservative so if we take the partial derivative with respect to y of f of x and that's equal to the partial derivative with respect to x of f of y then we're in good shape and then if we do the same with the z derivative and the x derivative here and then if we do f y d z and then d f z e y if all three of these are satisfied we're good what's the y derivative of f sub x well edx is a function of x so it's just a constant and derivative of cosine is negative sign so we have e the x negative sign of y and then the constant of front is z here so we have plus z and let's see if that's see if that's equal to the x derivative of f of y.
01:43
And it is, right? negative here, positive here, positive here, negative here.
01:47
So that checks out.
01:51
Z derivative of f sub x.
01:53
Well, nothing here is concerned with it...