public static SymbolicVariable DiffBFunction(SymbolicVariable fv, string parameter)
{
var pa = fv.GetFunctionParameters()[0];
var ps = SymbolicVariable.Multiply(pa, pa);
var func = fv.FunctionName;
var dpa = pa.Differentiate(parameter);
if (string.Equals(func, "asin", StringComparison.OrdinalIgnoreCase))
{
//asin(x) → 1 / sqrt(1-x^2)
return(SymbolicVariable.Parse(dpa.ToString() + "/sqrt(1-(" + ps.ToString() + "))"));
}
if (string.Equals(func, "acos", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/sqrt(1-(" + ps.ToString() + "))"));
}
if (string.Equals(func, "atan", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse(dpa.ToString() + "/(" + ps.ToString() + "+1)"));
}
if (string.Equals(func, "acot", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(" + ps.ToString() + "+1)"));
}
if (string.Equals(func, "asec", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse(dpa.ToString() + "/(sqrt(1-1/(" + ps.ToString() + "))*" + ps.ToString() + ")"));
}
if (string.Equals(func, "acsc", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(sqrt(1-1/(" + ps.ToString() + "))*" + ps.ToString() + ")"));
}
#region hyperbolic functions
if (string.Equals(func, "asinh", StringComparison.OrdinalIgnoreCase))
{
//asin(x) → 1 / sqrt(x^2+1)
return(SymbolicVariable.Parse(dpa.ToString() + "/sqrt(" + ps.ToString() + "+1)"));
}
if (string.Equals(func, "acosh", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/sqrt(" + ps.ToString() + "-1)"));
}
if (string.Equals(func, "atanh", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse(dpa.ToString() + "/(1-(" + ps.ToString() + "))"));
}
if (string.Equals(func, "acoth", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(" + ps.ToString() + "-1)"));
}
if (string.Equals(func, "asech", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(sqrt(1/" + ps.ToString() + "-1)*" + ps.ToString() + ")"));
}
if (string.Equals(func, "acsch", StringComparison.OrdinalIgnoreCase))
{
return(SymbolicVariable.Parse("-" + dpa.ToString() + "/(sqrt(1/" + ps.ToString() + "+1)*" + ps.ToString() + ")"));
}
#endregion
throw new SymbolicException(fv.FunctionName + " differentiation not implemented yet");
}