Answer
$$ f'(x)= -4e^{-4x+9}.$$
Work Step by Step
Recall that $(e^x)'=e^x$
Since we have
$$ f(x)=e^{-4x+9}$$
then the derivative $ f'(x)$, using the chain rule, is given by
$$ f'(x)=e^{-4x+9}(-4x+9)'=-4e^{-4x+9}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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: 23
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