The tanh function is a standard math function in C, defined in the math.h header file. It is used to calculate the hyperbolic tangent of a given value x.

The hyperbolic tangent function, denoted tanh(x), is defined as:

tanh(x) = (e^x - e^(-x)) / (e^x + e^(-x))

where e is the base of the natural logarithm.

The tanh function takes a single argument of type double, which represents the value whose hyperbolic tangent is to be calculated. The function returns a double value, which represents the calculated hyperbolic tangent.

Here's an example usage of the tanh function to calculate the hyperbolic tangent of a given input:

#include <stdio.h>
#include <math.h>

int main() {
    double x = 0.75;
    double hyperbolic_tangent = tanh(x);
    
    printf("The hyperbolic tangent of %f is %f\n", x, hyperbolic_tangent);
    
    return 0;
}

In this example, the tanh function is used to calculate the hyperbolic tangent of 0.75, which is stored in the x variable. The calculated hyperbolic tangent is then stored in the hyperbolic_tangent variable, and printed to the console using the printf function.

Note that the tanh function is only defined for real values of x. Also note that the hyperbolic tangent function grows very quickly for large positive or negative values of x, so it is important to be aware of potential overflow issues when working with large values.