#### Answer

$\dfrac {\tan x+xsec^{2}x}{5\sqrt [5] {\left( x\tan x\right) ^{4}}}$

#### Work Step by Step

$\dfrac {d}{dx}\left( \sqrt [5] {x\tan x}\right) =\dfrac {1}{5}\left( x\tan x\right) ^{\dfrac {1}{5}-1}\times \dfrac {d}{dx}\left( x\tan x\right) =\dfrac {\left( \dfrac {d}{dx}\left( x\right) \right) \times \tan x+\left( \dfrac {d}{dx}\left( \tan x\right) \right) xx}{5\sqrt [5] {\left( x\tan x\right) ^{4}}}=\dfrac {\tan x+xsec^{2}x}{5\sqrt [5] {\left( x\tan x\right) ^{4}}}$