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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)#

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