f-x-1-x-1-x-1-x-1-x-f-x-

Question Number 211944 by liuxinnan last updated on 25/Sep/24

f (x) = \frac{\sqrt{1 + x} - \sqrt{1 - x}}{\sqrt{1 + x} + \sqrt{1 - x}} f^{^{'}} (x) = ?

Answered by efronzo1 last updated on 25/Sep/24

f (x) = \frac{{(\sqrt{1 + x} - \sqrt{1 - x})}^{2}}{2 x}

f (x) = \frac{2 - 2 \sqrt{1 - x^{2}}}{2 x} = \frac{1}{x} - \sqrt{\frac{1}{x^{2}} - 1}

f^{'} (x) = - \frac{1}{x^{2}} - \frac{- \frac{2}{x^{3}}}{2 \sqrt{\frac{1}{x^{2}} - 1}}

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