Question

Obtenha a derivada da função f(x) = x-1/x-2

Answer 1

Resposta:

Explicação passo-a-passo:

$\boxed{\dfrac{d}{dx}\bigg(\dfrac{f(x)}{g(x)}\bigg)=\dfrac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}}$

$h(x)=\dfrac{f(x)}{g(x)}\ \therefore\ h(x)=\dfrac{x-1}{x-2}\\\\ \dfrac{d}{dx}\big(h(x)\big)=\dfrac{(x-2)\frac{d}{dx}(x-1)-(x-1)\frac{d}{dx}(x-2)}{(x-2)^2}=\\\\ =\dfrac{(x-2)(1)-(x-1)(1)}{(x-2)^2}=\dfrac{x-2-x+1}{(x-2)^2}\ \therefore\\\\ \boxed{h'(x)=-\dfrac{1}{(x-2)^2}}$