5.2 Euler’s Number + Natural Logs – Centennial Math Department

Here we will be exploring how to derive Eulers number (e≈ 2.718281828459045…) and natural logs (logs with the base e, “ln” you may have seen this in previous problems). Very important to know how to derive these so that you can ANTI-derive in future integral problems applying “e”.

What is Eulers Number?

Derivative of “e”

We are basically using chain rule to derive e. e^x where “e” is f(x) and “x” is g(x), therefore chaining f'(g(x))*g'(x)-> e^x *1 = e^x

Derivative of Natural Logs

Essentially, the derivative of ln is just taking the reciprocal of the inner function. Sometimes using log rules if required to derive a natural log with a rational inner function.