Let H be the half-plane H = {(x, y) R2 : x > 0}. Let G : H R3 be given by G(x, y) = (ylnx, xe^y, sin(xy)) for any (x, y) H. Compute the differential matrix of G for an arbitrary input (x, y) H. Then find the best affine approximation of G at the point (1, ).