Verify that f of x comma y equal to x squared times y squared plus x is a potential function for velocity field v of x comma y equal to angle bracket 2xy squared plus 1, comma 2x squared y. In order for this function to be a potential function for the velocity field, we need to find the gradient of this function. So the gradient of f, which is equal to the vector fx comma fy. That gradient needs to be equal to the velocity field v.

So if we find fx it's going to be equal to, let's see, y squared times 2x plus 1. We're taking the partial with respect to x of f of x comma y, and for our second component, fy, that would be equal to x squared times 2y end dangle bracket, which means that the gradient is equal to 2xy squared plus 1, comma 2x squared y. Because this is equal to the velocity field v. This is in fact a potential function for that velocity field.