Question

Найти производную функцию y=(x^2+1)/(x^2-4)

Answer 1

$y = frac{ x^{2} + 1}{x^{2} - 4} \ y' = frac{(x^{2} + 1)' * (x^{2} - 4) - (x^{2}+1) * (x^{2} - 4)'}{(x^{2} - 4)^{2}} = frac{2x * (x^{2} - 4) - 2x*(x^{2}+1)}{(x^{2} - 4)^{2}} = frac{2x(x^{2} - 4 - x^{2} - 1)}{(x^{2} - 4)^{2}} \ = frac{-10x}{(x^{2} - 4)^{2}}$