Math Exponential functions Natural exponential function

Natural exponential function

The natural exponential function is often referred to as e-function. The name comes from the Euler number $e$, which forms the basis of the exponential function for an e-function. The e-function has the function equation:



The Euler number is denoted by $e$ and, like $\pi$ is a constant, irrational number. The Euler number has the value $e = 2,7182818...$.


The derivative of the e-function $f(x)=e^x$ is also $f'(x)=e^x$. The following applies:

This is the e-function with $f(x)=e^x$:



  • The range of values $W=[0,\infty]$ and the domain $D=\mathbb{R}$ (real numbers)
  • The e-function has no zeros, because the x-axis is an asymptote (graph approaches, but never reaches)
  • The intersection with the y-axis is at $P(0|1)$.
  • The graph monotonically increases