Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 6 - Applications of Integration - 6.8 Logarithmic and Exponential - 6.8 Exercises: 51

Answer

$$ - 20x{e^{ - 10{x^2}}}$$

Work Step by Step

$$\eqalign{ & \frac{d}{{dx}}\left( {{e^{ - 10{x^2}}}} \right) \cr & {\text{by }}\frac{d}{{dx}}\left( {{e^{u\left( x \right)}}} \right) = {e^{u\left( x \right)}}u'\left( x \right) \cr & = {e^{ - 10{x^2}}}\frac{d}{{dx}}\left( { - 10{x^2}} \right) \cr & = {e^{ - 10{x^2}}}\left( { - 20x} \right) \cr & {\text{simplify}} \cr & = - 20x{e^{ - 10{x^2}}} \cr} $$
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