Question

Найти производную:
(x-1)/((x^2)+5)*(sqrt((x^2)+5))

Answer 1

$y=frac{x-1}{(x^2+5)cdot sqrt{x^2+5}}=frac{x-1}{(x^2+5)^{frac{3}{2}}}\\y'=frac{1cdot (x^2+5)^{frac{3}{2}}-(x-1)cdot frac{3}{2}cdot (x^2+5)^{frac{1}{2}}cdot 2x}{(x^2+5)^3}=frac{x^2+5-3x(x-1)}{(x^2+5)^{frac{5}{2}}}=frac{-2x^2+3x+5}{(x^2+5)^2sqrt{x^2+5}}$