Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 4 - Calculating the Derivative - 4.3 The Chain Rule - 4.3 Exercises - Page 225: 28


$f'(x) = (32t)(4t^2+7)^{-1/2} $

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 = 4t^2+7 $ $f(u) = 8u^{1/2}$ Derivate the function: $f'(u) = 4u^{-1/2}u'$ Now let's find u' $u' = 8t$ Then undo the substitution, simplify and get the answer: $f'(x) = 4(8t)(4t^2+7)^{-1/2} $ $f'(x) = (32t)(4t^2+7)^{-1/2} $
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