Question

Derivada de
f(x)= $\frac{sen x}{ \sqrt[5]{x^2} }$

Answer 1

derivada do senx = cosx

Regra do quociente

$( \frac{x}{g} )' = \frac{x'.g-g'.x}{g^2}$

$f'= \frac{cosx. \sqrt[5]{x^2} - \frac{2.senx}{5 \sqrt[5]{x^3 } } }{( \sqrt[5]{x^2})^2}$

$f'= \frac{cosx.x ^\frac{2}{5} - \frac{2.senx}{5 \sqrt[5]{x^3 } } }{(x^ \frac{4}{5}) }$

$f'= \frac{-2senx}{5^ \frac{7}{5} } + \frac{cosx}{x^ \frac{2}{5} }$