The chaotic behavior in the real dynamics of a one parameter family of nonlinearfunctions is studied in the present paper. For this purpose, the function f (x) = xex /( x -1) 0, xR {1} is considered. The fixed points, periodic points and their nature areinvestigated for the function f (x) . Bifurcation is shown to occur in the dynamics of f (x) .Period doubling, which is a route of chaos in the real dynamics, is also shown to take place inthe real dynamics of f (x) . The orbits of the dynamics of f (x) are graphically representedby time series graphs. Moreover, the chaotic behavior in the dynamics of f (x) is found bycomputing positive Lyapunov exponents.