00:01
We know that the vector field f equals to p i plus q j is conservative if del p by del y equals to del q upon del x.
00:21
Now, here the vector field f of x comma y equals to y square minus 2 x minus 2 x i plus 2 x y j.
00:38
So, now here p is equals to p is equals to y square minus 2 x and q is equals to q is equals to 2 x y.
00:52
So, partial derivative of p with respect to y that will be equals to with respect to y.
01:00
So, here this will be equals to 2 y and partial derivative of q with respect to x is 2 x.
01:12
So, since since del p by del y equals to del q by del x therefore, f x y vector field is conservative it is conservative.
01:30
Now, here f of x comma y equals to integration of y square minus 2 x the after integrating this is equals to this is equals to y square x minus twice of x square by 2 plus constant term c.
01:55
Now, here this can be written as f of x comma y equals to y square x minus x square plus constant term c.
02:09
So, now partial derivative of this function with respect to y is given by given by twice of y x and plus c dash y this is y...
