>>10906237there is only one function that meets this description, , that's literally why it's such an important question.
As you might imagine, it's also very easy to do integrals of this function.
So oftentimes we will get more complex functions in terms of a sum of 's and do the integral that way.
In general it's extremely important.
There's also something perhaps just as important called the logarithm. Just as multiplication "undoes" division, and subtraction "undoes" addition, the logarithm "undoes" an exponential.
So for example:
notice the subscript? The way you would say that is "log base e". For any given exponential, you have a logarithm with the corresponding base. So for example, you can have "log base 10", or "log base 7", depending on what exponential you're countering. This is just a function like any other (although with it's own unique properties), think of it just like a sine or cosine function or something.
"log base e" is given a special notation "ln", this is called "the natural logarithm". It's the most important by far.
It turns out that we can express the derivatives of any other exponential in terms of the natural logarithm. (remember how I said the derivative of an exponential was itself multplied by a constant? That constant happens to be the natural logarithm of that same exponential. So the derivative of is
As far as how to calculate "e", that's something you can look into yourself. There are several different methods
