F yexy x2 xexyy3SolutionHi Fx yexy x2 Fy xexy y3 We tak

Solution

Hi,
F(x) = ye^{(xy) +} x²
F(y) = xe^(xy) + y³

We take the derivative of the first function with respect to x and the second one with respect to why then we compare them, if they are equal they are conservative:

F\'(x) = 2 x + e^{(x y)} y²
F\'(y) = e^{(x y)} x² + 3 y²

F\'(x) does not equal F\'(y) so they are not conservative