// iksNaIks.cpp  function f(x) = x^x
#include <iostream>
using namespace std;

double iksNaIks(double x) {
	return pow(x, x);
}
double derivationIksNaIks(double v) {		// f'(x) = x^x * (ln (x) + 1)
	return (iksNaIks(v) * (log(v) + 1));
}
double derivation2IksNaIks(double v) {		// f''(x) = x^x * ((ln(x) + 1)^2 + 1/x)
	return (iksNaIks(v) * (pow((log(v) + 1),2) + 1/v));
}

double ableitungOne(double x) {
	double deltaX = 0.0001;
	return ((iksNaIks(x) - iksNaIks(x - deltaX)) / deltaX);
}

double ableitungTwo(double x) {
	double deltaX = 0.0001;
	return ((ableitungOne(x) - ableitungOne(x - deltaX)) / deltaX);
}
int main() {
	double x = 0.01;
	for (int u = 1; u < 200; u++) {
		cout << x << ' ' << pow(x, x) << endl;
		x += 0.01;
	}

	

	
	double x1 = 0.1, x2 = 2.0;
	for(double x = x1; x < x2;){
		
		double deltaX = 0.1;
		cout << " x " << x << " derIksNaIks: " << derivationIksNaIks(x) << endl;
		for (int u = 0; u < 3; u++) {
			deltaX /= 10;
			cout << deltaX << " " << (iksNaIks(x) - iksNaIks(x - deltaX)) / deltaX << endl;
		}
		cout << endl;
		x += 0.1;
	}
	x1 = 0.01, x2 = 2.0;
	for (double x = x1; x < x2;) {
		double deltaX = 0.1;
		cout << " x " << x << " der2IksNaIks: " << derivation2IksNaIks(x) << endl;
		for (int u = 0; u < 3; u++) {
			deltaX /= 10;
			cout << deltaX << " " << (derivationIksNaIks(x) - derivationIksNaIks(x - deltaX)) / deltaX << endl;
		}
		cout << endl;
		x += 0.1;
	}

	for (double x = x1; x < x2;) {
		cout << " x " << x << " Ableitung " << ableitungTwo(x) << endl;
		x += 0.1;
	}
}

Davon abgesehen ist eine numerische Berechnung der Ableitung für kaum jemanden interessant.