How can I note transformation step?
Typically these things are set as comments (on the right) of the actual structure:
\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{align}
0 &\stackrel{!}{=} (d_{P,f}^2)'\\
&= -2 x_p + 2x -2y_p f'(x) + \bigl(f(x)^2 \bigr)'\\
&= -2 x_p + 2x -2y_p f'(x) + 2 f(x) \cdot f'(x) \rlap{\hspace*{2em}(Chain rule)} \\
&= -2 x_p + 2x -2y_p (2ax+b) + ((ax^2+bx+c)^2)'
\end{align}
\end{document}
The fact that the comment is set in \rlap
automatically turns it into text mode, but also does not affect the horizontal placement of the entire structure
A combination of \substack
-- a macro provided by the amsmath
package -- and \mathclap
(provided by the mathtools
package) may be able to deliver what you want:
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{align}
0 &\stackrel{!}{=} (d_{P,f}^2)'\\
&= -2 x_p + 2x -2y_p f'(x) + \bigl(f(x)^2 \bigr)'\\
&\stackrel{\mathclap{\substack{\text{Chain}\\\text{Rule}}}}{=}
-2 x_p + 2x -2y_p f'(x) + 2 f(x) \cdot f'(x) \\
&= -2 x_p + 2x -2y_p (2ax+b) + ((ax^2+bx+c)^2)'
\end{align}
\end{document}
If you intention was making Chain rule
as narrow as possible...
\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
\begin{align}
0 &\stackrel{!}{=} (d_{P,f}^2)'\\
&= -2 x_p + 2x -2y_p f'(x) + \left (f(x)^2 \right )'\\
&\overset{\mathclap{\begin{array}{c}\mbox{\tiny Chain}\\[-6pt] \mbox{\tiny rule}\end{array}}}{=} -2 x_p + 2x -2y_p f'(x) + 2 f(x) \cdot f'(x)\\
&= -2 x_p + 2x -2y_p (2ax+b) + ((ax^2+bx+c)^2)'
\end{align}
\end{document}
Of course, one can correct also vertical spacing between 2nd and 3rd line, but I am not sure if this your wish.