What is the derivative of ##lnx^lnx##?
The derivative of a logarithm (be it natural or base-10) ##ln[f(x)]## is given by the formula:
f'(x) / f(x)
Where f'(x) is the derivative of the original function f(x).
Ok, keep that aside for a while.
Now, going back to logarithms properties, we have that ##ln(x)^m## = ##m.ln(x)##
Then, we have in your example:
##ln(x)^ln(x)## = ##ln(x)## . ##ln(x)##
Deriving it consists on deriving a product, which consists on:
Derivative of the first function times the original second function
PLUS
Derivative of the second function times the original first function
Like this:
##1/x . ln(x)## + ##ln(x) + 1/x## = ##2.ln(x)/x##
🙂
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