<s>[INST] Sigmoid Function Typically sigmoid function is calculated as 
    1/(1 + exp(-x))

I see sometimes it is calculated as
    1 - 1/(1 + exp(x))

or even
   exp(x)/(1 + exp(x))

Could you clarify the difference please?
 [/INST] $$
\frac
{1}{1+\exp(-x)}
=
\frac
{1}{1+e^{-x}}
=
\frac
{1}{1+e^{-x}}
\cdot
\frac
{e^x}{e^x}
=
\frac
{e^x}{e^x+1}
=
\frac
{e^x}{1+e^x}
=
\frac
{\exp(x)}{1+\exp{x}}
$$
and also
$$
1-\frac
{1}{1+\exp(x)}
=
1-\frac
{1}{1+e^{x}}
=
\frac{1+e^x}{1+e^x}
-
\frac{1}{1+e^x}
=
\frac{(1+e^x)-1}{1+e^x}
=
\frac
{e^x}{1+e^x}
=
\frac
{\exp(x)}{1+\exp{x}}
$$
</s>