The sigmoid function, also called the sigmoidal curve or logistic function, is the function y = 1/(1 + e^(-x)). It has derivative (d y)/(d x) | = | [1 - y(x)] y(x) | = | e^(-x)/(1 + e^(-x))^2 | = | e^x/(1 + e^x)^2 and indefinite integral integral y d x | = | x + ln(1 + e^(-x)) | = | ln(1 + e^x).
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