Question

Encontre a derivada:
f(x)=x−1/x−2

Answer 1

F(x)=x-1/x-2

f'(x)=[(x-1)'.(x-2)-(x-1).(x-2)']/(x-2)²

f'(x)=[(x-2)-(x-1)]/(x-2)²

f'(x)=-1/(x-2)²

_______________________________

Answer 2

Regra do quociente:

((x-1)' × (x-2) - (x-1) × (x-2)')/(x-2)²
((1-0) × (x-2) - (x-1) × (1-0))/(x-2)²
(1 × (x-2) - (x-1) × 1)/(x-2)²
((x-2) - (x-1))/(x-2)²
(x - 2 - x + 1)/(x-2)²
(-2 + 1)/(x+2)²
-1/(x-2)²

Resultado final:

$- \frac{1}{(x - 2) {}^{2} }$

Espero ter ajudado ;)