Question

Qual a derivada de 4/x-1?

Answer 1

$\mathrm{y=\dfrac{f(x)}{g(x)}\ \to\ y'=\dfrac{f'(x).g(x)-g'(x).f(x)}{{[g(x)]}^2}}\\\\\\ \mathrm{y=\dfrac{4}{x-1}\ \to\ y'=\dfrac{\frac{d}{dx}(4).(x-1)-\frac{d}{dx}(x-1).4}{(x-1)^2}}\\\\\\ \mathrm{y'=\dfrac{0.(x-1)-1.4}{(x-1)^2}\ \to\ \boxed{\mathbf{y'=-\dfrac{4}{(x-1)^2}}}}$