Question

determinar derivada da função:

$\sqrt[3]{x^3+3}$

Answer 1

 Olá!

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