Question

Encontre a derivada da função Y= $\sqrt[5]{x}$

Answer 1

$y = \sqrt[5]{x} \\ y' = \frac{d}{dx} ( \sqrt[5]{x}) \\ y' = \frac{d}{dx} (x {}^{ \frac{1}{5} } ) \\ y' = \frac{1}{5} x {}^{ \frac{1}{5} - 1 } \\ y '= \frac{1}{5} x {}^{ - \frac{4}{5} } \\ y '= \frac{1}{5} \: . \: \frac{1}{x {}^{ \frac{4}{5} } } \\ y' = \frac{1}{5x {}^{ \frac{4}{5} } } \\ \boxed{y' = \frac{1}{5 \sqrt[5]{x {}^{4} } } }$

att. yrz