Question

cos-¹(x-x-¹/x+x-¹) diffrentiat ir

Answer 1

you can see your answer

Answer 2

$Let,\\\,\;y=cos^{-1}(\frac{x-x^{-1}}{x+x^{-1}})\\\;\\y=\cos^{-1}(\frac{x^{2}-1}{x^{2}+1})\\\;\\let\;x=\tan\theta\;\to\;\theta=\tan^{-1}x\\\;\\y=\cos^{-1}(\frac{\tan^{2}\theta-1}{\tan^{2}\theta+1})\\\;\\y=\cos^{-1}(\cos2\theta)\\\;\\y=2\theta\\\;\\y=2\tan^{-1}x\\\;\\\text{diff both sides w.r.t x}\\\;\\\frac{dy}{dx}=2\frac{d(\tan^{-1}x)}{dx}\\\;\\\frac{dy}{dx}=\frac{2}{1+x^{2}}$