Answer
\[\frac{{dy}}{{dx}} = \frac{1}{{x\ln 10}}\]
Work Step by Step
\[\begin{gathered}
y = {\log _{10}}x \hfill \\
\hfill \\
Differentiate,{\text{ use }}\frac{d}{{dx}}\left[ {{{\log }_a}u} \right] = \frac{1}{{\ln a\left( u \right)}}{u^,} \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{1}{{\,\left( {\ln 10} \right)\,\left( x \right)}}\,\left( {{x^,}} \right) \hfill \\
\hfill \\
multiply \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{1}{{x\ln 10}} \hfill \\
\hfill \\
\end{gathered} \]
