Question

Найти производную.
$y=2 sqrt{ frac{1- sqrt{x} }{1+ sqrt{x} } }$

Answer 1

$y=2 sqrt{ frac{1-sqrt{x}}{1+ sqrt{x}}} ; ; ,; ; ; (sqrt{u})'=frac{1}{2sqrt{u}}cdot u'; ,; ; ( frac{u}{v})'= frac{u'v-uv'}{v^2} \\y'=2cdot frac{1}{2 sqrt{frac{1-sqrt{x}}{1+sqrt{x}}}} cdot frac{-frac{1}{2sqrt{x}}cdot (1+sqrt{x})-(1-sqrt{x})cdot frac{1}{2sqrt{x}}}{(1+sqrt{x})^2} =\\= sqrt{frac{1+sqrt{x}}{1-sqrt{x}}}cdot frac{-1-sqrt{x}-1+sqrt{x}}{2sqrt{x}}=-frac{1}{sqrt{x}}cdot sqrt{frac{1+sqrt{x}}{1-sqrt{x}}}$