Answer
$$\frac{(\ln 10)10^{\sqrt{u}}}{ 2\sqrt{u} }$$
Work Step by Step
Given $$h(u)= 10^{\sqrt{u}}$$
Take $\ln$ for both sides
\begin{align*}
\ln h(u)&=\ln 10^{\sqrt{u}}\\
&= \sqrt{u} \ln 10
\end{align*}
Then
\begin{align*}
\frac{'h(u)}{h(u)} &=\frac{\ln 10}{ 2\sqrt{u} }\\
h'(u)&=h(u)\frac{\ln 10}{ 2\sqrt{u} }\\
&=\frac{(\ln 10)10^{\sqrt{u}}}{ 2\sqrt{u} }
\end{align*}
