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Sigmoid and Its Derivative is a easy coding interview question covering math, deep learning — the kind asked at FAANG (Facebook/Meta, Apple, Amazon, Netflix, Google) and AI-first companies like Anthropic, OpenAI, and Nvidia.
Implement the sigmoid activation function and its derivative, used in logistic regression and neural network output layers.
sigmoid(x) = 1 / (1 + e^(-x)) sigmoid_derivative(x) = sigmoid(x) * (1 - sigmoid(x))
Example: sigmoid(0) = 0.5, sigmoid(2) ~= 0.88, sigmoid(-2) ~= 0.12
For numerical stability: when x < 0, use e^x / (1 + e^x) to avoid overflow in e^(-x).
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