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: 38


$$ f'(x)=-6e^{5-6x}\sec^2 (e^{5-6x})$$

Work Step by Step

Recall that $(e^x)'=e^x$ Recall that $(\tan x)'=\sec^2 x$. Since we have $$ f(x)= \tan(e^{5-6x})$$ then the derivative $ f'(x)$, using the chain rule, is given by $$ f'(x)=\sec^2 (e^{5-6x})(e^{5-6x})'=-6e^{5-6x}\sec^2 (e^{5-6x})$$
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