Measurements of the total and differential cross sections $d\ensuremath{\sigma}/d{p}_{T}^{B}$ and $d\ensuremath{\sigma}/d{y}^{B}$ for ${B}^{+}$ mesons produced in $pp$ collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ are presented. The data correspond to an integrated luminosity of $5.8\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ collected by the CMS experiment operating at the LHC. The exclusive decay ${B}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}$, with $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, is used to detect ${B}^{+}$ mesons and to measure the production cross section as a function of ${p}_{T}^{B}$ and ${y}^{B}$. The total cross section for ${p}_{T}^{B}>5\text{ }\text{ }\mathrm{GeV}$ and $|{y}^{B}|<2.4$ is measured to be $28.1\ifmmode\pm\else\textpm\fi{}2.4\ifmmode\pm\else\textpm\fi{}2.0\ifmmode\pm\else\textpm\fi{}3.1\text{ }\text{ }\ensuremath{\mu}\mathrm{b}$, where the first uncertainty is statistical, the second is systematic, and the last is from the luminosity measurement.