Single Variable Calculus, Chapter 7, Review Exercises, Section Review Exercises, Problem 36

Differentiate $\displaystyle F(z) = \log_{10} (1 + z^2)$


$
\begin{equation}
\begin{aligned}

F'(z) =& \frac{d}{dz} [\log_{10} (1 + z^2)]
\\
\\
F'(z) =& \frac{1}{(1 + z^2) \ln 10} \cdot \frac{d}{dz} (1 + z^2)
\\
\\
F'(z) =& \frac{1}{(1 + z^2) \ln 10} \cdot 2z
\\
\\
F'(z) =& \frac{2z}{(1 + z^2) \ln 10}


\end{aligned}
\end{equation}
$