Logistic function

• How to Find the Inverse of a Sigmoid Equation
  Invert the standard logistic sigmoid by taking the log-odds: x = ln(y/(1−y)). This guide derives the formula, its domain, and scaled variants.
• How to Find the Derivative of the Logistic Function
  Differentiate the logistic sigmoid using the chain rule, obtain σ′(x) = σ(x)(1 − σ(x)), and adapt the result to scaled logistic functions.