Quiz PHPID

Derivative.java

public class Derivative {
    private static String calculate(int n) {
        if (n <= 1) return "";
        StringBuilder res = new StringBuilder();
        res.append(recX(n - 1, false));
        res.append(recDX(n - 2));
        return res.toString();
    }
    
    private static String recX(int n, boolean decrease) {
        StringBuilder res = new StringBuilder();
        if (n == 0) {
            res.append("x");
            return res.toString();
        }
        if (decrease) {
            res.append("x^{");
            res.append(recX(n - 1, false));
            res.append("-1}");
            return res.toString();
        }
        res.append("x^{");
        res.append(recX(n - 1, false));
        res.append("}");
        return res.toString();
    }
    
    private static String recDX(int n) {
        StringBuilder res = new StringBuilder();
        if (n == 0) {
            res.append("(\\ln(x)+1)");
            return res.toString();
        }
        res.append("(");
        res.append(recX(n, false));
        res.append("\\ln(x)");
        res.append(recDX(n - 1));
        res.append("+");
        res.append(recX(n, true));
        res.append(")");
        return res.toString();
    }
    
    public static void main(String []args){
        System.out.println(calculate(4));
    }
}

derivative.php

<?php
function derivative($n) {
    $y = recX($n - 1);
    $x = recDX($n - 2);
    return sprintf("%s%s", $y, $x);
}

function recX($n, $decrease=false) {
    if ($n == 0) return "x";
        
    if ($decrease) {
        $x = recX($n -1);
        return sprintf("x^{%s-1}", $x);
    }
    $x = recX($n -1);
    return sprintf("x^{%s}", $x);
}

function recDX($n) {
    if ($n == 0) return "(ln(x)+1)";
    
    $y = recx($n);
    $ym = recX($n, true);
    $dx = recDX($n - 1);
    return sprintf("(%s\ln(x)%s+%s)", $y, $dx, $ym);
}
?>

derivative.py

def derivative(n):
    y = recx(n - 1)
    return '{} {}'.format(y, recdx(n - 2))

def recx(n, mi=False):
    if n == 0:
        return 'x'
    if mi:
        return 'x^{' + recx(n - 1) + ' - 1}'
    return 'x^{{{0}}}'.format(recx(n - 1))

def recdx(n):
    if n == 0:
        return '(\ln(x) + 1)'
    y = recx(n)
    ym = recx(n, True)
    return '({} \ln(x) {} + {})'.format(y, recdx(n - 1), ym)