Hello I am having trouble understand the following in my notes;
It was an example;
Q: Is $$v=K(-yi+xj)$$ a conservative vector field?
If it was, then $$K(-yi+xj)=\nabla \psi$$
Here is where I am confused;
Next line says
$$\partial \psi/\partial x= -Ky$$ which implies $\psi(x,y)=-Kxy+f(y)$
$$\partial \psi / \partial y= Kx$$ which implies $\psi(x,y)=Kxy+g(x)$
and so we are able to conclude that it is not conservative from inspection.
But how did we do the partial derivatives. I thought the partial of \psi w.r.t x would mean we treat everything except x constant, etc. Can anyone please help to explain this to me?