Question

Qual a derivada de x/x^2+1 ?

Answer 1

Regra do quociente
$f(x)= \frac{x}{x^2+1} \\ f'(x)= \frac{(x^2+1).1-x(2x)}{(x^2+1)^2} \\ f'(x)= \frac{x^2+1-2x^2}{(x^2+1)^2} \\ f'(x)= \frac{1-x^2}{(x^2+1)^2}$