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
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Verified answer
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
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Verified answer
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:
Espero ter ajudado ;)