00:01
The question asked to find whether this vector function is a conservative vector field.
00:08
And the way to check that is to find whether the partial derivative of r in respect to d .y is equivalent to the partial derivative of q in respect to d .c.
00:22
And to find if the partial derivative of d .r in respect to dx is equivalent to partial derivative of d .p.
00:30
In respect to d z and finally the partial derivative of q in respect d x is equivalent to the partial derivative of p in respect to d y with p being y sine z q being x sine z and r is xy cosine c so the partial derivative r in respect to d y xy cosine c since we're finding the partial derivative of r in respect to d y xy cosine c since we're finding the partial derivative of to d, y, x and cosine z act as constants.
01:08
So then the derivative of this expression would be x cosine c.
01:15
And the partial derivative of q in respect to dz, x, x sine z, which again, x will remain as a constant.
01:26
And we're going to find the partial derivative in respect to z.
01:29
So this would be x cosine z.
01:32
So these two are equivalent.
01:37
Now we need to find a partial derivative of r respect to x, which is xy cosine z...