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: 26


$$ f'(x)= 2x(1+x)e^{2x}.$$

Work Step by Step

Recall the product rule: $(uv)'=u'v+uv'$ Recall that $(e^x)'=e^x$ Since we have $$ f(x)=x^2 e^{2x}$$ then the derivative $ f'(x)$, using the chain and product rules, is given by $$ f'(x)= (x^2)'e^{2x}+x^2(e^{2x})'=2xe^{2x}+2x^2e^{2x}=2x(1+x)e^{2x}.$$
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