If f (x )= cot^-1 ⁡ ( x^x-x^-x2 ), then f^ ' (1 )=

Question

Accepted Answer

Correct answer: D. (d) Given, f (x )= cot^-1 ⁡ ( x^2-x^-x2 ) Let y= cot^-1 ⁡ ( x^2x-12x^x ) Put x^x= tan ⁡ ⇒y= cot^-1 ⁡ ( tan^2 ⁡ -12 tan ⁡ ) y= - cot^-1 ⁡ ( cot ⁡2 ) y= -2 y= -2 tan^-1 ⁡ (x^x ) ∴ dy dx=- 21+x^2x x^x (1+ log ⁡x ) So, dy dx at x=1= -21+ (1 )^2 (1+ log ⁡1 )=- 22 1=-1

$If f (x) = cot^{- 1} (\frac{x ^{x} - x ^{- x}}{2}), then f^{’} (1) =$

Solution

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