# Drawing a sigmoid function and its derivative in tikz

I created a graph of the sigmoid function using the following tikz code:

\documentclass{minimal}
\usepackage{tikz,pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}%
[
grid=major,
xmin=-6,
xmax=6,
axis x line=bottom,
ytick={0,.5,1},
ymax=1,
axis y line=middle,
]
[
blue,%
mark=none,
samples=100,
domain=-6:6,
]
(x,{1/(1+exp(-x))});
\end{axis}
\end{tikzpicture}
\end{document}


Is it possible to add the derivative of the sigmoid function to the graph using a red dotted line, including a legend in the topright corner for both lines without leaving the tikz environment?

Sigmoid function: σ = 1/(1+exp(-x))

Derivative: σ(x)(1−σ(x)

The arguably most convenient way is to declare functions with the declare function key, and plot them.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[declare function={sigma(\x)=1/(1+exp(-\x));
sigmap(\x)=sigma(\x)*(1-sigma(\x));}]
\begin{axis}%
[
grid=major,
xmin=-6,
xmax=6,
axis x line=bottom,
ytick={0,.5,1},
ymax=1,
axis y line=middle,
samples=100,
domain=-6:6,
legend style={at={(1,0.9)}}
]
\legend{$\sigma(x)$,$\sigma'(x)$} • @bjornvandijkman You're welcome! You do not necessarily need to do a parametric plot here, \addplot[blue,mark=none] {sigma(x)}; will also work.