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Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
The exponential function is the unique function f ... = f(x) follows from the condition that f′(0) = 1 and the definition of the derivative as follows: ...
Toggle Derivatives of exponential and logarithmic functions subsection. 3.1 Logarithmic derivatives. ... The derivative of the function () = (() ...
The exponential function () = is the unique differentiable function of a complex variable for which the derivative equals the function = and () = Power series definition [ edit ]
For example, the exponential function is the function which is equal to its own derivative everywhere, and assumes the value 1 at the origin. However, one may equally well define an analytic function by its Taylor series. Taylor series are used to define functions and "operators" in diverse areas of mathematics. In particular, this is true in ...
The exponential function may be defined as ... can also be exponentiated. An example is the derivative operator of calculus, /, which is a linear ...
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group.
It gives simple arithmetic formulas to accurately compute values of many transcendental functions such as the exponential function and trigonometric functions. It is the starting point of the study of analytic functions , and is fundamental in various areas of mathematics, as well as in numerical analysis and mathematical physics .