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: 32


$f'(t) = -\dfrac{5(2t+3)}{2\sqrt{ t^2+3t+1}}=-\dfrac{10t+15}{2\sqrt{ t^2+3t+1}}$

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 $u = t^2+3t+1$ $f(u) = u^{-5/2}$ Derivate the function: $f'(u) = -\dfrac{5}{2} u^{7/2}u'$ Now let's find u' $u' = 2t+3$ Then undo the substitution, simplify and get the answer: $f'(t) = -\dfrac{5(2t+3)}{2\sqrt{ t^2+3t+1}}=-\dfrac{10t+15}{2\sqrt{ t^2+3t+1}}$
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