Question

Найти производные y'(x) заданных функций:
$y=x*sqrtfrac{1+x^{2} }{1-x^{2} }$

$frac{1}{tg^{2}*2x }$

Answer 1

$1); ; y=xcdot sqrt{frac{1+x^2}{1-x^2}}\\y'=sqrt{frac{1+x^2}{1-x^2}}+xcdot frac{1}{2sqrt{frac{1+x^2}{1-x^2}}}cdot frac{2x(1-x^2)-(1+x^2)cdot (-2x)}{(1-x^2)^2}=\\=sqrt{frac{1+x^2}{1-x^2}}+frac{x}{2}cdot sqrt{frac{1-x^2}{1+x^2}}cdot frac{4x}{(1-x^2)^2}\\2); ; y=frac{1}{tg^22x}\\y'=frac{-2, tg2xcdot frac{1}{cos^22x}cdot 2}{tg^42x}=-frac{4, tg2x}{cos^22xcdot tg^42x}=-frac{4cos2x}{sin^32x}$