Originally Posted by
zeg that is for when a is a constant in this case, it is a function of x, so here's my stab at it:
$\displaystyle y = tan(x)^{sec(x)}$
$\displaystyle ln(y) = sec(x)\cdot ln(tan(x))$
now take your derivative, d/dx
$\displaystyle (ln(y))^{\prime} = (sec(x))^{\prime}\cdot ln(tan(x)) + sec(x)\cdot (ln(tan(x)))^{\prime}$
$\displaystyle \frac{y^{\prime}}{y} = sec(x)\cdot tan(x)\cdot ln(tan(x)) + csc(x)$
so
$\displaystyle y^{\prime} = [sec(x)\cdot tan(x)\cdot ln(tan(x)) + csc(x)]\cdot tan(x)^{sec(x)}$
that seems messy though. maybe there's some nice simplifications in there somewhere.