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: 21


$f'(x) = \dfrac{x+1}{\sqrt{x^2+2x+9}}(\cos {\sqrt{x^2+2x+9}})$

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 $u = \sqrt{x^2+2x+9}$ $f(u) = \sin u$ Derivate the function: $f'(u) = \cos u$ Now let's find u' $u' = \dfrac{x+1}{\sqrt{x^2+2x+1}}$ Then undo the substitution, simplify and get the answer: $f'(x) = \dfrac{x+1}{\sqrt{x^2+2x+9}}(\cos {\sqrt{x^2+2x+9}})$
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