Question

y=(x^4+1)/(x^4-1)
найти производную

Answer 1

$y=\dfrac{x^4+1}{x^4-1}$

$y'=\dfrac{(x^4+1)'(x^4-1)-(x^4+1)(x^4-1)'}{(x^4-1)^2} =\dfrac{4x^3(x^4-1)-(x^4+1)\cdot4x^3}{(x^4-1)^2} =\\=\dfrac{4x^7-4x^3-4x^7-4x^3}{(x^4-1)^2} =\boxed{-\dfrac{8x^3}{(x^4-1)^2} }$