ABSTRACT
The exponential function e x was introduced in Chapter 3 as an example of a function defined by a limit. Its occurrence throughout mathematics, together with its inverse, the natural logarithmic function ln x, is sufficiently frequent to justify studying e x and ln x separately. In the first part of this chapter the differentiability property of e x is established by means of a definition of the exponential function which is different than but equivalent to the one used in Chapter 3 and makes use of that definition together with a geometrical argument and the idea that a function can be defined in terms of a series involving powers of x. The differentiability properties of the natural logarithmic function are then deduced from those of the exponential function by using the fact that dy/dx = 1/(dx/dy).
