Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 386: 35


$$ R'(s)= 2 s^{\ln s-1}\ln s.$$

Work Step by Step

Since $ R(s)=s^{\ln s}$, applying $\ln $ on both sides, we get $$\ln R(s)=\ln s^{\ln s}=\ln s \ln s=(\ln s)^2$$ Hence the derivative, using the chain rule, is given by $$ R'(s)/R(s)=2\ln s (\ln s)'=\frac{2\ln s}{s} .$$ Then, we have $$ R'(s)=\frac{2\ln s}{s} R(s)=\frac{2\ln s}{s} s^{\ln s} =2 s^{\ln s-1}\ln s.$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.