Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 34


$$ f'(t)= \frac{1}{2} \frac{1}{\sqrt{t}} e^{\sqrt{t}} .$$

Work Step by Step

Recall that $(e^x)'=e^x$ Since we have $$ f(t)= e^{\sqrt{t}}$$ then the derivative $ f'(t)$, using the chain rule, is given by $$ f'(t)=e^{\sqrt{t}} (\sqrt{t})'=\frac{1}{2} \frac{1}{\sqrt{t}} e^{\sqrt{t}} .$$
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