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The inverse of the natural log function lnx is ex
A function must be one to one to have an inverse and the log function is.

I am not sure if that is what you are asking.
The derivative of ex is itself.
That is to say if f(x)=ex then f'(x)=ex

If you are asking about the derivative of lnx, it is 1/x
and if you look at logb x=1/(xlnb)

Not sure which one you are looking for.

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