Derivative of the logit function I have plotted a logit function and its derivative. My first question is that how can I interpret the derivative graph of the logit function and second, why in logit function, the second derivative becomes the logit function itself?  


The second derivative of the logit function is not equal to itself. Look:
$$l(x)=\ln\bigg(\frac{x}{1-x}\bigg)$$
$$l(x)=\ln(x)-\ln(1-x)$$
Then differentiate:
$$l'(x)=\frac{1}{x}+\frac{1}{1-x}$$
Then differentiate again:
$$l''(x)=-\frac{1}{x^2}-\frac{1}{(1-x)^2}$$
The second derivative of the logit function is a completely different function.
