How do you differentiate #f(x) = sec(tan(sec(tan(x))))#?

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Answer 1 · 2015-06-05T22:33:23

#f(x) = sec{tan[sec(tanx)]}#

If you write this as:
#f{g[h(i(x))]}#

then

#f'(x) = f'{g[h(i(x))]}*g'[h(i(x))]*h'[i(x)]*i'(x)#

and

#f'(secu) = (secutanu)*u'(x)#
and
#f'(tanu) = (sec^2u)*u'(x)#

so

#f'(x) = #
#sec{tan[sec(tanx)]}tan{tan[sec(tanx)]}#
#* sec^2(sec(tanx))#
#* sec(tanx)tan(tanx)#
#* sec^2x#