Question

$frac{x^{2}+1 }{x^{2}-1}$ Производную пожалуйста

Answer 1

$y=frac{x^{2}+1 }{ x^{2}-1 }\\y'=frac{(x^{2}+1)*'(x^{2} -1)-(x^{2}+1)*(x^{2}-1)'}{(x^{2}-1)^{2}}=frac{2x*(x^{2}-1)-2x(x^{2}+1)}{(x^{2}-1)^{2}} =frac{2x^{3}-2x-2x^{3}-2x}{(x^{2}-1)^{2}}=-frac{4x}{(x^{2}-1)^{2}}$