Cauchy–Riemann equation on differntiability 
I have found that: 
$U_x = -\exp(y)\sin(x) $
$U_y = \exp(y)\cos(x) $
$V_x = \exp(y)\cos(x) $
$V_y = \exp(y)\sin(x) $
I need to show that $U_x=V_y$ and $U_y=-V_x$, however these aren't satisfied? does that mean $f$ is not differentiable?

Correct.  If the same expression that appears on the right side were $f(y+ix)$ rather than $f(x+iy)$ then it would be differentiable.
