Question

calcular derivada de f(x) = raiz cúbica de x^2 com x = 8

Answer 1

$\large{f(x)= \sqrt[3]{x^2}}\\\\\large{f(x)=x^{ \frac{2}{3}}}\\\\f'(x)= \dfrac{2}{3}\cdot{x^{\frac{2}{3}-1}} \\\\\\f'(x)= \dfrac{2}{3}\cdot{x^ {-\frac{1}{3} }}\\\\\\f'(8)= \dfrac{2}{3}\cdot(8)^ {-\frac{1}{3}}\\\\\\f'(8)= \dfrac{2}{3 \sqrt[3]{8}}\\\\\\f'(8)= \dfrac{2}{3\cdot2}\\\\\\\boxed{f'(8)=\dfrac{1}{3}}$