Question

if y=tan^-1 (1+x)/(1-x) then dy/dx=?

please solve the problem it is urgent
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Answer 1

$\huge\bf{\mid{\overline{\underline{ANSWER:-}}\mid}}$

$y = {\tan}^{-1} [\frac{1+x}{1-x}] \\ \\ We \: know.. \\ \\ {\tan}^{-1}(a) + {\tan}^{-1}(b) = {\tan}^{-1} [\frac{a + b}{1 - ab}] \\ \\ Using \: same \: formula.... \\ \\ {\tan}^{-1}(1) + {\tan}^{-1}(x) = {\tan}^{-1} [\frac{1 + x}{1 - x}] \\ \\ So \: y = {\tan}^{-1} [\frac{1 + x}{1 - x}] \: will \: be \: directly \: converted \: to \implies \\ \\ y = {\tan}^{-1}[ \frac{\pi}{4} ] + {\tan}^{-1}[x] \\ \\ \frac{dy}{dx} = 0 + \frac{d}{dx} ({\tan}^{-1}[x] ) \\ \\ \huge\boxed{ \therefore \frac{dy}{dx} = \frac{1}{1+{x}^{2}} }$