Representation e^x \,
Inverse \ln x \,
Derivative e^x \,
Indefinite Integral e^x + C \,
The graph of y = ex is upward-sloping, and increases faster as x increases. The graph always lies above the x-axis but can get arbitrarily close to it for negative x; thus, the x-axis is a horizontal asymptote. The slope of the tangent to the graph at each point is equal to its y coordinate at that point. The inverse function is the natural logarithm ln(x); because of this, some old texts refer to the exponential function as the antilogarithm.
Sometimes the term exponential function is used more generally for functions of the form cbx, where the base b is any positive real number, not necessarily e. See exponential growth for this usage.
In general, the variable x can be any real or complex number, or even an entirely different kind of mathematical object; see the formal definition below. Part of a series of articles on
The mathematical constant e
Natural logarithm · Exponential function
Applications in: compound interest · Euler's identity & Euler's formula · half-lives & exponential growth/decay
Defining e: proof that e is irrational · representations of e · Lindemann–Weierstrass theorem
People John Napier · Leonhard Euler
1 Formal definition