Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise - Page 464: 29


$2vsec^{2}(4^{v^{2}}) 4^{v^{2}}ln4$

Work Step by Step

Let $L'(v)$ be the derivative of the function $tan(4^{v^{2}})$. $L'(v)=\frac{d}{dv}tan(4^{v^{2}})$ $=sec^{2}4^{v^{2}}\frac{d}{dv}(4^{v^{2}})$ $=sec^{2}4^{v^{2}} 4^{v^{2}}ln4\frac{d}{dv}{(v^{2}})$ $=2vsec^{2}(4^{v^{2}}) 4^{v^{2}}ln4$
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