radix

$${f}{\left({\mathtt{x}}\right)} = {\frac{{\mathtt{x}}}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}}$$

f'(x) =   $${\frac{{\mathtt{1}}}{\left({{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}}$$

Gruß radix !

Hier auch noch einmal die Tabelle :

What is a  quadragintillion ?

$${\mathtt{\,-\,}}{\frac{{\frac{{\frac{{\mathtt{16}}}{{\mathtt{40}}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{15}}}{{\mathtt{40}}}}\right)}{{\mathtt{30}}}}}{{\mathtt{40}}}} = {\mathtt{\,-\,}}{\frac{\left({\mathtt{16}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{40}}\right)}{\left({\mathtt{40}}{\mathtt{\,\times\,}}{\mathtt{40}}{\mathtt{\,\times\,}}{\mathtt{30}}\right)}} = {\frac{{\mathtt{1}}}{{\mathtt{5}}}}$$

$${\mathtt{\,-\,}}{\frac{\left({\frac{{\mathtt{16}}}{{\mathtt{40}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{15}}}{{\mathtt{40}}}}\right)}{\left({\frac{{\mathtt{30}}}{{\mathtt{40}}}}\right)}} = {\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{5}}}} = -{\mathtt{0.2}}$$

$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{3}}}{{\mathtt{8}}}} = {\frac{{\mathtt{7}}}{{\mathtt{24}}}} = {\mathtt{0.291\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{3}}}{{\mathtt{8}}}} = {\frac{{\mathtt{16}}}{{\mathtt{24}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{{\mathtt{24}}}} = {\frac{{\mathtt{7}}}{{\mathtt{24}}}}$$

733.55    =>   9.5 %

    x         =>  100 %            $${\mathtt{x}} = {\frac{{\mathtt{733.55}}{\mathtt{\,\times\,}}{\mathtt{100}}}{{\mathtt{9.5}}}}$$   =  7 721.579

$${\frac{{\mathtt{733.55}}{\mathtt{\,\times\,}}{\mathtt{100}}}{{\mathtt{9.5}}}} = {\mathtt{7\,721.578\: \!947\: \!368\: \!421\: \!052\: \!6}}$$

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{6}} = {\mathtt{0}}$$

$${\mathtt{x}} = {\mathtt{0.5}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{{\mathtt{0.5}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}}}$$

$${\mathtt{x}} = {\mathtt{0.5}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{\mathtt{6.25}}}}$$               =>    x1 =  0.5 +2.5 = 3

                                            =>    x2  =  0.5 -2.5  = -2

 x² - x -6 = (x + 2)*(x - 3 )

(x+2)*(x-3) = 0                =>    x1 = -2      and   x2 = +3

$${\mathtt{124\,566\,415}}{\mathtt{\,-\,}}{\mathtt{50\,000\,000}}{\mathtt{\,-\,}}{\mathtt{15\,000\,000}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}} = {\mathtt{59\,566\,416}}$$

=         74 566 415    - 15 000 000  + 1

=        59 566 415  +  1   =   59 566 416

$${\frac{{\mathtt{65\,192}}}{{\mathtt{8}}}}{\mathtt{\,\times\,}}{\mathtt{9}} = {\mathtt{73\,341}}$$   [MYR]

(5+3)*2 = 8*2 = 16

5+2*3 = 5 + 6 = 11

both is right !