Question

determine a derivada:
f(x)= (x²+1\3x-1)

Answer 1

$f(x) = \frac{x^2+1}{3x-1}$

usando a regra do quociente
$\boxed{( \frac{U}{V} )' =\frac{U'*V - U*V'}{V^2} }}$

logo
$U = x^2+1\\\\U' =2x\\\\\ V=3x-1\\\\V'=3$

substituindo na regra do quociente
$f'(x)= \frac{2x*(3x-1) -(x^2+1)*3}{(3x-1)^2}\\\\f'(x)= \frac{6x^2-2x-3x^2-3}{(3x-1)^2} \\\\ \boxed{\boxed{f'(x)= \frac{3x^2-2x-3}{(3x-1)^2}} }}$