00:01
In this problem of vector fields, we have to determine whether the vector field is conservative or not and if it is conservative we have to find a potential function for the vector field.
00:12
So we have the vector field f of xy is equal to 2x i plus 2y j divided with x square plus y square to whole square.
00:26
From here we would first find the value of m that is the coefficient of i.
00:30
So this is 2x divided with x squared plus y square to whole square and the value of n that is the coefficient of j which is 2y divided with x square plus y square.
00:43
This is x square plus y square to whole square.
00:49
And now we have to find the value of partial differentiation of m with respect to y and partial differentiation of n with respect to x.
00:56
So, now we have to do the differentiation of this term with respect to y.
01:06
So this value would be minus and this is 1 divided with, we have to increase the power by 1, so this is x squared plus y square to power 3.
01:16
Now this is 2x, so this value would be 2x because this is treated as constant...