Question

A derivada da função f (x)  x - 1 / x2 - 1 no ponto x= 1 é: obs a função esta em forma de fração

Answer 1

$f(x)=\dfrac{x-1}{x^2-1}=\dfrac{x-1}{(x-1)(x+1)}=\dfrac{1}{x+1}\\\\\\f'(x)=\dfrac{(1)'(x+1)-(x+1)'(1)}{(x+1)^2}=\dfrac{-1}{(x+1)^2}\\\\\\f'(1)=-\dfrac{1}{((1)+1)^2}=-\dfrac{1}{2^2}=-\dfrac14$