Chapter 7: Transcendental Functions - Section 7.3 - Exponential Functions - Exercises 7.3 - Page 391: 77

$$ y ^{\prime}=\frac{1}{\ln 10}$$

Given $$ y =\log _{10} e^x $$ Since $$\log_{a}z=\frac{\ln z}{\ln a}$$ So, we have \begin{aligned} y& =\log _{10} e^x\\ &=\frac{\ln e^x}{\ln 10}\\ &=\frac{x\ln e}{\ln 10} \\ &=\frac{x }{\ln 10}\\ &\Rightarrow y^{\prime}=\frac{1}{\ln 10} \end{aligned}