: the derivation

## since "e" is a constant, and the derivative of any constant is 0, we will consider taking the derivative of e

^{x}. Its derivative is as follows...

## What does this mean? We see the graph of e

^{x }is:

^{}

## The derivative of a function enables us to find the slope of any point of that function. For example, if f(x)=x

^{2}, then dy/dx=2x is the slope of the curve at any point x.

## Here, we see that if x=1, then the slope (also the tangent of the curve at a given point) is two. If x=2, then the slope will be 4 and so on according to y=2x. Getting back to how this affects e

^{x}, we find that the derivative of e^{x}is also e^{x}. The graphs of which are identical: