Forum:
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
Try Wolfram Alpha?
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.
Thanks for the help!
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
Integral of bell curve
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.
I've forgotten everything
Demiurge - Sun, 05/30/2021 - 12:49Hi,
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:
https://commons.wikimedia.org/wiki/File:Improperintegral2.png
The fancy symbols are a mathematical way of describing how to calculate that area.
--Jon