Tool to calculate the values of the exponential function exp(x) e(x) e^x and solve the calculations related to the function or the constant e=2.71818…
Exponential - dCode
Tag(s) : Functions
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
The definition of the exponential function is the solution of the equation $ f' = f $ with $ f(0) = 1 $, i.e. the function which is its own derivative and which has the value 1 at 0.
The exponential function is denoted by exp that is, by default, based on the number $ e \approx 2.71828\ldots $ (check also the decimals of the number e).
Example: $ \exp(7) = e^7 \approx 1096.633 $
The $ e^x $ notation is sometimes ambiguous, because $ e $ may be used as a variable, prefer using the $ \exp(x) $ notation.
The exponential has several remarkable properties
$ \exp(0) = 1 \\ \exp(1) = e \approx 2.71828\ldots \\ e^(x+y) = e^x \times e^y \\ (e^x)^b = e^{bx} \\ \ln(\exp(x)) = x \\ \exp(\ln(x)) = x $$
The derivative of the exponential function is the exponential function itself
$$ f(x) = \exp(x) \iff f'(x) = \exp(x) $$
The exponential is related to the exponentiation by the formula:
$$ a^b = e^{b\ln(a)} $$
In the complex plane, the exponential has several other properties (complex exponential form):
$$ \exp(i x) = \cos x + i \sin x \\ \exp(a + i b) = \exp(a) ( \cos b + i \sin b ) $$
The exponential function can be defined as a series expansion based on factorial and exponentiation:
$$ \exp(x)=\sum _{{n=0}}^{{\infty }}{x^{n} \over n!} $$
dCode retains ownership of the "Exponential" source code. Except explicit open source licence (indicated Creative Commons / free), the "Exponential" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Exponential" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Exponential" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
The copy-paste of the page "Exponential" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Exponential on dCode.fr [online website], retrieved on 2024-12-03,