How do you find the derivative of # (ln(ln(ln(x))) #?

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Answer 1 · 2016-09-01T14:55:27

#=1/((ln(ln(x))))#X#1/ln(x)#X#1/x#, #x> e#.

Apply function of function rule.

#(ln(ln(ln(x))))'#

#=i/(ln(ln(x))# #(ln(ln(x))'#

#=1/((ln(ln(x))(ln(ln(x))# #(ln(x))'#

#=1/((ln(ln(x))# #1/ln(x)# #1/x#

ln x is differentiable for x > 0.

ln(ln(x) is differentiable, for ln(x) > 0, and so, for # x > 1#.

ln(ln(ln(x))) is differentiable for

ln(ln(x)) > 0, meaning ln(x) > 1, and so, x > e..