Conservative Vector Field without using potential function

Question

I am really new to this topic and was tasked to show that G (x,y,z)=<z³−3y²e^3x, −2ye^3x+2cosz, 4+3xz²−2ysinz> is conservative without using any potential function. How do I pull this off? I have no idea where to start with this one. Any help would be much appreciated

Answer 1

Compute the curl. A conservative field has a zero curl, ∇ x G = 0.