Using 281 pb^{-1} of data collected at the \psi(3770) resonance at the CLEO-c detector, we measure the purely leptonic decay of the D+ meson using the channel D^+ \to \mu^+ \nu_\mu. We use a method which takes advantage of the intrinsic hermeticity of the CLEO-c detector in order to reconstruct the missing momentum and energy, which is then interpreted as the signal neutrino. The resolution of the missing energy is improved by fully reconstructing the hadronically decaying D meson as a combination of \pi^\pm,K^\pm, K_S \to \pi^+ \pi^-, \pi^0 \to\gamma\gamma and \eta\to\gamma\gamma . Low energy showers which cannot be associated with \pi^0\to\gamma\gamma or \eta\to\gamma\gamma are rejected. By replacing the signal leptonic decay channel with a well measured D+ hadronic decay such as D^+ \to K^- \pi^+ \pi^+ and requiring the missing energy to be small, we can use the same generic reconstruction technique to measure systematic errors that may affect the overall efficiency of the leptonic analysis. In order to reduce our systematic errors, we scale our leptonic yields by the D^+ \to K^- \pi^+ \pi^+ yield and find the branching fraction in terms of the D^+ \to K^- \pi^+ \pi^+ branching fraction. We find B( D^+ \to \mu^+ \nu_\mu) = (3.90 \pm 0.55_stat \pm 0.10_syst )\times 10^{-4} for the branching fraction of the process, from which we extract f_{D+} = (209.7 \pm 14.6_stat \pm 2.7_syst ) MeV.