Question

How do you differentiate `f(x) = e^(e^x)`?

Answer 1

`f'(x) = e^(x+e^x)`

Explanation:

`f(x) = e^(e^x)`
`ln(f(x)) = ln(e^(e^x))`
`ln(f(x)) = e^xlne`
`ln(f(x)) = e^x`
`d/dx(ln(f(x))) = d/dx(e^x)`

`1/f(x)*f'(x) = e^x`

`f'(x) = e^x * f(x)`

`f'(x) = e^x * e^(e^x)`

`f'(x) = e^(x+e^x)`