Is this vector field conservative? $\displaystyle F(x)=(y+z, x+y, x+z)$
If it is, how do you find the potential field?
Thsi vector field is conservative because when you calculate the curl (set up the Jacobian) it is equal to zero.
This means there is a unique potential function whose differentiation yields the vector field that you mentioned.
Now, to find the potential FUNCTION (not "field") you take the anti-derivative of each term.
The final potential function according to my calculations is:
$\displaystyle F(x,y,z)=xy+zx+\frac{y^{2}}{2}+\frac{z^{2}}{2}$
Could somebody confirm?