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: 22


$f'(x) = (30x^2+45)(2x^3+9x)^4$

Work Step by Step

In order to derivate this function you have to apply the chain rule Let's make a «u» substitution to make it easier $u = 2x^3+9x$ $f(u) = u^5$ Derivate the function: $f'(u) = 5u^4u'$ Now let's find u' $u' = 6x^2+9$ Then undo the substitution, simplify and get the answer: $f'(x) = 5(6x^2+9)(2x^3+9x)^4$ $f'(x) = (30x^2+45)(2x^3+9x)^4$
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