Given-f-x-tan-x-find-df-x-dx-x-k-where-pi-2-lt-k-lt-pi-

Question Number 133610 by benjo_mathlover last updated on 23/Feb/21

Given f (x) = ∣ \tan x ∣, find

\frac{df (x)}{dx} ∣_{x = k} where \frac{π}{2} < k < π

Answered by guyyy last updated on 23/Feb/21

Answered by liberty last updated on 23/Feb/21

\Rightarrow we have y^{2} = \tan^{2} x

\Rightarrow 2 y y^{'} = 2 \tan x \sec^{2} x

\Rightarrow y^{^{'}} = \frac{\tan x \sec^{2} x}{∣ \tan x ∣}; where on interval

\frac{π}{2} < k < π \Rightarrow \tan k < 0

\frac{df (x)}{dx} ∣_{x = k} = \frac{\tan k \sec^{2} k}{- \tan k} = - \sec^{2} k

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