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: 14

Answer

$f'(x) = -(10+30x)(4-2x-3x^2)^4$

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 $u = 4-2x-3x^2$ $f(u) = u^5$ Derivate the function: $f'(u) = 5u^4u'$ Now let's find u' $u' = -2-6x$ Then undo the substitution, simplify and get the answer: $f'(x) = 5( (-2-6x)$ $f'(x) = -(10+30x)(4-2x-3x^2)^4$
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