Question

$derivada f(x) = \sqrt[3]{x^5}$

Answer 1

$Regra\ da\ Cadeia\\\\ f(x)=(x^5)^{ \frac{1}{3} }\\\\\\u=x^5\\\\\\f(u)=u^{ \frac{1}{3} }\\\\\\f'(u)= \dfrac{1}{3}u^{ \frac{1}{3}-1 }\\\\\\f'(u)= \dfrac{1}{3}u^{- \frac{2}{3} }\\\\\\f'(u)= \dfrac{1}{3u^{ \frac{2}{3} }} \\\\\\u(x)=x^5\\\\u'(x)=5x^4\\\\\\f'(x)=u'(x)\cdot{f'(u)}\\\\\\f'(x)=5x^4\cdot \dfrac{1}{3x^5^{ \frac{2}{3}}}\\\\\\f'(x)= \dfrac{5x^4}{3x^5^{ \frac{2}{3} }}$