Show that G-> is conservative

Question

Show that G^->(x, y, z) =〈3y² + 2/z , 6xy + 2z/√y , 4√y − 2x/z², x, y, z > 0 is conservative

(a) without using any potential function for G^->;

(b) by finding all potential functions for G^->

Answer 1

a. The curl of G should be zero. Take the curl and show that it ends up as a zero. Curl definition is relatively simple and can be found online.

b. Set G equal to the negative gradient of a potential V. This should give you a general equation for V. You are essentially guessing the antiderivative here.