Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 781: 30


$$ R_v= -\frac{2v}{k}e^{-v^2/k}, \quad R_k= \frac{v^2}{k^2}e^{-v^2/k}. $$

Work Step by Step

Recall that $(e^x)'=e^x$ Recall that $(x^n)'=nx^{n-1}$ Since $ R=e^{-v^2/k}$, then by using the chain rule, we have $$ R_v= -\frac{2v}{k}e^{-v^2/k}, \quad R_k= \frac{v^2}{k^2}e^{-v^2/k}. $$
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