I can't find any insights online on how useful the graph of function $f(x)$ (on the $y$ axis) versus it's derivative $f'(x)$? (on the $x$ axis) does it provide some useful informations if any?

For example, I see that when I plot $\sin(x)$ against $\cos(x)$ the plot is a circle which is reminiscent of parametric equations.

My question is: Assuming the function is nice (nice in the common sense that it is continuous) does that kind of graph provide any useful information? What about this graph where $x(t) = f'(t)$: