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?  


Since you appear to be using Mathematica
logf[x_, a_, b_] := Log[a*x/(1 - b*x)]

With[{a = 1},
 Plot3D[logf[x, a, b], {x, 0, 1}, {b, 0, 1},
  ClippingStyle -> None,
  PlotPoints -> 100]]


The first derivative of logf with respect to x is
D[logf[x, a, b], x] // Simplify


Note that the first derivative is independent of a
Plot3D[1/(x - b*x^2), {x, 0, 1}, {b, 0, 1},
 ClippingStyle -> None]


The second derivative of logf with respect to x is
D[logf[x, a, b], {x, 2}] // Simplify


Plot3D[(-1 + 2*b*x)/(x^2*(-1 + b*x)^2), {x, 0, 1}, {b, 0, 1},
 ClippingStyle -> None,
 PlotPoints -> 100]


