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: 41


$$ f''(x)= 16 e^{4x-3}.$$

Work Step by Step

Recall that $(e^x)'=e^x$ Since we have $$ f(x)= e^{4x-3}$$ then the first derivative $ f'(x)$, using the chain rule, is given by $$ f'(x)= e^{4x-3}(4x-3)'=4 e^{4x-3}.$$ The second derivative $ f''(x)$ is given by $$ f''(x)= 4 e^{4x-3}(4x-3)'=16 e^{4x-3}.$$
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