Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 146: 15



Work Step by Step

In order to derivate this function you have to apply the chain rule Let's make an «u» substitution to make it easier $u = x^2+9x$ $f(u) = u^{-2}$ Derivate the function: $f'(u) = -2u^{-1}u'$ Now let's find u' $u' = 2x+9$ Then undo the substitution, simplify and get the answer: $f'(x) = -\dfrac{2(2x+9)}{x^2+9x}=\dfrac{-4x-18}{x^2+9x}$
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