Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.6 The Chain Rule - Exercises Set 2.6: 20

Answer

$f′(x)=12x^2\sec^2(x^3)\tan^{3}(x^3)$

Work Step by Step

$f(x)=tan^4(x^3)$ $f′(x)=4tan^{4−1}(x^3)×(\frac{d}{dx})(tan(x^3))$ $f′(x)=4tan^{3}(x^3)×sec^2(x^3)\times(\frac{d}{dx})(x^3)$ $f′(x)=4tan^{3}(x^3)×sec^2(x^3)\times3x^2$ $f′(x)=12x^2\sec^2(x^3)\tan^{3}(x^3)$
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