Change of Variables & the Jacobian · Medium problem

The transformation $x=e^u\cos v$, $y=e^u\sin v$ is applied near the point $(u,v)=(\ln 2,\ \pi/4)$. A tiny disk of radius $0.01$ centered there is mapped to a tiny region. Using the Jacobian as a local area-scaling factor, estimate the area of that image region.