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: 42


The third derivative $ f'''(x)$ is given by $$ f'''(x)= -27 e^{12-3x}.$$

Work Step by Step

Recall that $(e^x)'=e^x$ Since we have $$ f(x)= e^{12-3x}$$ then the first derivative $ f'(x)$, using the chain rule, is given by $$ f'(x)= e^{12-3x}(12-3x)'=-3 e^{12-3x}.$$ The second derivative $ f''(x)$ is given by $$ f''(x)= -3 e^{12-3x}(12-3x)'=9 e^{12-3x}.$$ The third derivative $ f'''(x)$ is given by $$ f'''(x)= 9e^{12-3x}(12-3x)'=-27 e^{12-3x}.$$
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