Basic exponential functions have the form `f(x) = b^x` where `b` is some positive number.
In this applet we see what `f(x) = b^x` looks like for various values of `b`, and we
see how `f'(x)` is related to `f(x)`. In particular, it turns out that
If `f(x) = b^x`, then `f'(x)` is proportional to `f(x)`.
That is, [`f'(x) = m_b f(x)`] for some number `m_b` that depends on `b`.
`m_b` is the slope of the line tangent to `y = b^x` through the point `(0, 1)`.
fact, coupled with the definition for `e` (see below) implies
If `f(x) = e^x`, then `f'(x) = e^x`.