Answer
$7e^{7x}$
Work Step by Step
Given $$y=e^{7x}.$$ We will apply the chain rule for the function $y=e^u$, where $u=7x$: $$\begin{aligned}
\frac{dy}{dx}&=u'e^u\\
\frac{dy}{dx}&=(7x)'e^{7x}\\
&=7e^{7x}.
\end{aligned}$$
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.3 Derivatives Of Inverse Functions; Derivatives And Integrals Involving Exponential Functions - Exercises Set 6.3 - Page 432: 13
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