: the derivation

since "e" is a constant, and the derivative of any constant is 0, we will consider taking the derivative of ex.  Its derivative is as follows...

What does this mean? We see the graph of ex is: 

The derivative of a function enables us to find the slope of any point of that function.  For example, if f(x)=x2, 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 ex, we find that the derivative of exis also ex.  The graphs of which are identical: