Derivative of the first function times the original second function PLUS Derivative of the second function times the original first function

Derivative of the first function times the original second function PLUS Derivative of the second function times the original first function

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

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