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

1 Answer
Mar 15, 2016

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)