exp — exponential function

1. Definition

Exponential function is the function of kind

e^x

where constant e is selected so that slope of the function at point x = 1 is 45°.

Exponential function is defined everywhere on real axis. Its graph is depicted below — fig. 1.

Fig. 1. Graph of the exponential function y = e^x.

Function codomain is positive half of the real axis: (0, +∞).

By definition:

e^lnx ≡ x

Negative argument:

e^−x = 1 /e^x

Sum and difference of arguments:

e^{x + y} = e^x e^y
e^{x − y} = e^x/e^y

Product of arguments:

e^xy = (e^x)^y

Base change:

a^x = e^{x lna}

Exponent derivative:

e^x′ = e^x

Indefinite integral of the exponent:

∫ e^x dx = e^x + C

where C is an arbitrary constant.

To calculate exponent of the number:

exp(−1);

To get exponent of the complex number:

exp(−1+i);

To get exponent of the current result:

exp(rslt);

To get exponent of the number z in calculator memory:

exp(mem[z]);

Exponent of the real argument is supported in free version of the Librow calculator.

Exponent of the complex argument is supported in professional version of the Librow calculator.