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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It is the logarithmic function.
The exponential function, in the case of the natural exponential is f(x) = ex, where e is approximately 2.71828. The logarithmic function is the inverse of the exponential function. If we're talking about the natural logarithm (LN), then y = LN(x), is the same as sayinig x = ey.
Logarithmic equation
An inverse of a function is found by swapping the x and y variables. For example: the straight line function y = 2x, has an inverse of x = 2y. This can be rearranged into y = x/2. Now take the function y = ex. The inverse is: x = ey. Unfortunately, there is no easy way to rearrange this to be y = {something}. So the logarithm function was created to handle this, and now the function {x = ey} can be written as y = ln(x).
The inverse function means the opposite calculation. The inverse function of "add 6" would be "subtract 6".