Question

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

Answer 1

`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`