What we call "the exponential function" is a special function indeed. The construction below is designed to show you why a number such as [math]e = 2.718281828\dots[/math] should be so fundamental in calculus. You can discover that, when the base of [math]y = a^x[/math] is [math]a = e[/math], two important things happen: 1) the tangent line at [math]x=0[/math] has slope [math]1[/math], and 2) the graph of [math]f[/math] and [math]f'[/math] coincide.