Posted: Feb 22, 2012 8:12 am
E and the Natural Logarithm LN

One of the numbers that comes up a lot in physics, is e and its associated natural logarithm ln. For both of these I will again point you to the Wolfram site to read upon the basics:

e at Wolfram
Natural logarithm ln

e is another irrational number like π; it comes up a lot if you are studying physics or mathematics, and I suggest that you read at least the basics on e. Maybe someone else might take up a discussion on the various mathematical irrational numbers like e and π.

In mathematics e is a lot of times interchanged with exp as a symbol. Let's first see the functions:

Then the derivatives will be:

If you will notice, in the derivative of the natural logarithm, the constant a does not feature anywhere. If you know anything about logarithms, then you will know that:

ln(a) is itself a constant, and so its derivative is 0. So we are left with the derivative of the second term, which is ln(x).

Some basic mathematical tricks with the above functions:

for