# Chapter 6 - Inverse Functions - Review - Exercises - Page 505: 24

$$\frac{(\ln 10)10^{\sqrt{u}}}{ 2\sqrt{u} }$$

#### 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*}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.