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: 24


$f'(x) = (336x^{3})(3x^4+2)^{-5}$

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 = 3x^4+2 $ $f(u) = -7u^{-4}$ Derivate the function: $f'(u) = 28u^{-5}u'$ Now let's find u' $u' = 12x^{3}$ Then undo the substitution, simplify and get the answer: $f'(x) = 28(12x^{3})(3x^4+2)^{-5}$ $f'(x) = (336x^{3})(3x^4+2)^{-5}$
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