If f(x) = ( _ x x) ( _ x x)^ - 1 , then f'(2) = - Vidyadip

MCQ

If $f(x) = ({\log _{\cot x}}\tan x){({\log _{\tan x}}\cot x)^{ - 1}},$ then $f'(2) = $

A
$2$
✓
$0$
C
${1 \over 2}$
D
$-2$

✓

Answer

Correct option: B.

$0$

b
(b) Obviously, $f(x) = {({\log _{\cot x}}\tan x)^2}$

$ = {({\log _{\cot x}}{(\cot x)^{ - 1}})^2} \Rightarrow f'(x) = 0$ .

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