$\displaystyle

\sqrt{sec\sqrt{x}}

$

$\displaystyle

= (sec(x^\frac{1}{2}))^\frac{1}{2}

$

$\displaystyle

= \frac{1}{2}(sec(x^\frac{1}{2}))^\frac{-1}{2}

$

$\displaystyle

= \frac{1}{2}(sec(x^\frac{1}{2}))^\frac{-1}{2} \cdot sec(x)^\frac{1}{2}tan(x)^\frac{1}{2} \cdot \frac{1}{2}x^\frac{-1}{2}

$

this the right path? thank u