Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.6 Trigonometric Functions - Exercises - Page 140: 19


$$ f'(x) =\frac{2\sec^2 x}{(1-\tan x)^2} .$$

Work Step by Step

Since $ f(x)= \frac{1+\tan x}{1-\tan x}$, then using the quotient rule, the derivative is giving by $$ f'(x)=\frac{(1-\tan x)(\sec^2x)- (1+\tan x)(-\sec^2x)}{(1-\tan x)^2} \\ =\frac{2\sec^2 x}{(1-\tan x)^2} .$$
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