Precision measurement of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">B</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>μ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mi>ν</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>and the pseudoscalar decay constant<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>f</mml:mi><mml:msup><mml:mi>D</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:msub></mml:math>

We measure the branching ratio of the purely leptonic decay of the ${D}^{+}$ meson with unprecedented precision as $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})=(3.82\ifmmode\pm\else\textpm\fi{}0.32\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, using $818\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of data taken on the $\ensuremath{\psi}(3770)$ resonance with the CLEO-c detector at the CESR collider. We use this determination to derive a value for the pseudoscalar decay constant ${f}_{{D}^{+}}$, combining with measurements of the ${D}^{+}$ lifetime and assuming $|{V}_{cd}|=|{V}_{us}|$. We find ${f}_{{D}^{+}}=(205.8\ifmmode\pm\else\textpm\fi{}8.5\ifmmode\pm\else\textpm\fi{}2.5)\text{ }\text{ }\mathrm{MeV}$. The decay rate asymmetry $\frac{\ensuremath{\Gamma}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})\ensuremath{-}\ensuremath{\Gamma}({D}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}\overline{\ensuremath{\nu}})}{\ensuremath{\Gamma}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})+\ensuremath{\Gamma}({D}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}\overline{\ensuremath{\nu}})}=0.08\ifmmode\pm\else\textpm\fi{}0.08$, consistent with no $CP$ violation. We also set 90% confidence level upper limits on $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}\ensuremath{\nu})&lt;1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\nu})&lt;8.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$.