Determine whether the vecteor field is conservative?

Question

Determine whether the vector field
F(x,y)=(2xy+sinhy)i+(x^2+x coshy)j
is conservative. If so, find the corresponding potential

Answer 1

potential= y*x^2+x*sinhy+const


If you take the grad of this it is the field. A field is conservative if there exists a potential such that you can take the grad and return the field.

So yes, it's conservative.

Answer 2

If the divergence is zero,the field is conservative.