Hello,

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!

Best,

Jay

Billy@ Tue, 01/19/2021 - 12:42I'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:

https://www.wolframalpha.com/input/?i=y+%3D+e%5Ex%2F%281%2Be%5Ex%29

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.

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Silmenume@ Thu, 01/21/2021 - 14:44Hey 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 allot...as many of the vocab words he's using are beyond me!

Best,

Jay

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Thanuir@ Tue, 04/20/2021 - 11:04There are many sigmoid functions, Wikipedia claims.

It seems one of them is the error function, the integral of the standard normal distribution (bell curve): https://en.wikipedia.org/wiki/Error_function

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: https://en.wikipedia.org/wiki/Normal_distribution and for the standard one, set mu to equal zero and sigma to equal one.

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