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

Answer 1

Emily Ammerman

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

#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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Answer 2

Aurora Alvarado

To differentiate ( f(x) = e^{e^x} ), you can use the chain rule. The derivative of ( e^{e^x} ) with respect to ( x ) is ( e^x \cdot e^{e^x} ). Therefore, the differentiation of ( f(x) ) is ( f'(x) = e^x \cdot e^{e^x} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.