Calculus, 10th Edition (Anton)

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: 18

Answer

$y' = -\dfrac{e^{1/x}}{x^2}$

Work Step by Step

In order to derivate this function you have to apply the chain rule Let's make a «u» substitution to make it easier $f(u) = e^u$ $u = \dfrac{1}{x}$ Derivate the function: $f'(u) = u'e^u$ Now let's find u' $u' =-\dfrac{1}{x^2} $ Then undo the substitution, simplify and get the answer: $y' = -\dfrac{e^{1/x}}{x^2}$
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