what is the first derivative of
sec^2 x ...
thanks =)
let $\displaystyle g(x)=\sec^{2}(x)$
$\displaystyle f(u)=u^2 \mbox{ and }u=\sec(x)$
$\displaystyle f'(u)=2u \mbox{ and } u'=\sec(x)\tan(x)$
then $\displaystyle g(x)=f(u)$
taking the derivative by the chain rule gives
$\displaystyle g'(x)=f'(u)\cdot u'=2u \cdot (\sec(x)\tan(x))$
but u is $\displaystyle u=\sec(x) $
so we get
$\displaystyle g'(x)=f'(u)\cdot u'=2u \cdot (\sec(x)\tan(x))=2\sec(x) \cdot (\sec(x)\tan(x))=2\sec^{2}(x)\tan(x)$