Question

qual a derivada de 1+3r2)/r2-r

Answer 1

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

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

aplicando isso
$f'(r)= \frac{(1+3r^2)'*(r^2-r) - (1+3r^2)*(r^2-r)'}{(r^2-r)^2} \\\\ f'(r)= \frac{(0+3*2r^{2-1})*(r^2-r) - (1+3r^2)*(2r^{2-1}-r^{1-1})}{(r^2-r)^2} \\\\ f'(r)= \frac{(6r)*(r^2-r) - (1+3r^2)*(2r-1)}{(r^2-r)^2} \\\\f'(r)= \frac{(6r^3-6r^2)-(6r^3 -3r^2+2r-1)}{(r^2-r)^2} \\\\\boxed{\boxed{f'(r)= \frac{-3r^2-2r+1}{(r^2-r)^2} }}$