Question

derive f(x)=³√(3x²+6x-2)²

Answer 1

Regra da Cadeia

$\boxed{f(g(x))'=f'(g(x))*g'(x)}$

Aplicando

$f(x)= \sqrt[3]{(3x^2-6x-2)^2}\\ \\f(x)= (3x^2-6x-2)^{ \frac{2}{3} }\\ \\f'(x)= \frac{2}{3} (3x^2-6x-2)^{- \frac{1}{3} }*(6x-6)\\ \\\boxed{\boxed{f'(x)= \frac{2(6x-6)}{3 \sqrt[3]{3x^2-6x-2} }} }$