Question

How do you find the derivative of `f(x) = e^(e^x)`?

Answer 1

`(dy)/(dx)=e^xe^(e^x)`

Explanation:

`f(x)=y=e^(e^x)`

Let `e^x=u`
`(du)/(dx)=e^x`

And `y=e^u`

`(dy)/(du)=e^u`

To find `(dy)/(dx)`, then
we know that `(dy)/(dx)=(dy)/(du)times(du)/(dx)=e^utimese^x=e^(e^x)timese^x=e^xe^(e^x)`