How do you differentiate f(x)=e^tan(lnx) using the chain rule?

1 Answer
Oct 29, 2015

f'(x) = (e^(tan(lnx))sec^2(lnx))/x

Explanation:

f'(x) = (e^(tan(lnx)))' = e^(tan(lnx)) * (tan(lnx))' = e^(tan(lnx)) * sec^2(lnx) * (lnx)' = e^(tan(lnx)) * sec^2(lnx) * 1/x

f'(x) = (e^(tan(lnx))sec^2(lnx))/x