Need Mathematician for help with Sigmoid Fuction

Silmenume's picture


I wondering if there is a mathematician here that can help me. I need help setting up an XP curve that looks like a Sigmoid Function. I've found the equation for it and even videos about it but what I really need to know is how to take the derivative at any given point. I know what these words mean, but I haven't a clue as to how they actually work i.e. I don't know how to take a derivative. So if someone could walk me through the process I'd really appreciate the help!



Billy's picture

I'm no mathematician, but when I need this kind of thing, I usually turn to Wolfram Alpha.

Example, if I go to Wolfram Alpha and search this equation: y=e^x/(1+e^x)

Then it gives me this page:

and scrolling down, where it says "Implicit Derivative" it shows the derivative of y with respect to x as
(dy(x))/(dx) = e^x/(1 + e^x)^2

Is that any help? If you enter your own sigmoid function, it should be able to do the same.

Silmenume's picture

Hey Billy,

Appreciate the link and the suggestion. Turns out that, having spoken to a friend, that what I really need is to take the integral of bell curve to get what I'm looking for. Something I'm wholly untrained to do. Fortunately my friend is currently taking Calculus 3 so is helping many of the vocab words he's using are beyond me!



Thanuir's picture

There are many sigmoid functions, Wikipedia claims.

It seems one of them is the error function, the integral of the standard normal distribution (bell curve):

If you the derivative of this, it is (as the fundamental theorem of calculus) simply the function that gives the standard normal distribution. See the formula at: and for the standard one, set mu to equal zero and sigma to equal one.

Demiurge's picture


I learned Calculus 1 and Calculus 2 and then took two Differential Equations classes. Unfortuately, that was amost 20 years ago and I haven't needed calculus since. I'm glad you found a friend that's currently taking Cal 3, because I've forgotten everything I ever learned! :)

Well, almost everything. If you imagine a line on an XY plane (also called a Cartesian Plane), then the *integral* is a measurement of the area beneath the line. It's demonstrated here:

The fancy symbols are a mathematical way of describing how to calculate that area.