Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

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*}
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