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: 54

Answer

$$e{x^{e - 1}} + {e^x}$$

Work Step by Step

$$\eqalign{ & \frac{d}{{dx}}\left( {{x^e} + {e^x}} \right) \cr & {\text{derivative of a sum}} \cr & = \frac{d}{{dx}}\left( {{x^e}} \right) + \frac{d}{{dx}}\left( {{e^x}} \right) \cr & {\text{evaluate the derivative}} \cr & = e{x^{e - 1}} + {e^x} \cr} $$
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