Question

Com o auxilio das propriedades operatorias das drivadas, calcule a derivada da função
f(x)= x/x+1

Answer 1

$f(x) = \frac{u(x)}{v(x)} = f'(x) = \frac{u'(x).v(x) -u(x).v'(x) }{[v(x)]^{2}}\\\\ f(x) = \frac{x}{x+1} = f'(x) = \frac{x'.(x+1) -x.(x+1)' }{(x+1)^{2}}\\\\ f'(x) = \frac{(x+1) - x}{(x+1)^{2}} = \frac{1}{(x+1)^{2}} = (\frac{1}{x+1})^{2} \\\\ \boxed{\boxed{f'(x) = (\frac{1}{x+1})^{2}}}$