Answer
$-10xe^{-5x^2}$
Work Step by Step
Given $$y= e^{-5x^2}.$$ We will apply the chain rule for $y=e^u$, where $u=-5x^2$: $$\begin{aligned}
\frac{dy}{dx}&=u'e^u\\
\frac{dy}{dx}&=(-5x^2)'e^{-5x^2}\\
&=-10xe^{-5x^2}.
\end{aligned}$$
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: 14
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