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Derivative Sigmoid function Calculator

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Calculates the derivative sigmoid function s'_a(x).

The sigmoid function is used in the activation function of the neural network.


a(gain)
x

\(
\normalsize Sigmoid\ function\ \varsigma_{\alpha}(x)\\
\varsigma_{\alpha}(x) = \large \frac{1}{1+e^{-\alpha x}} = \large \frac {\tanh(\alpha x /2) + 1}{2}\\
\normalsize \varsigma '_{\alpha}(x) = \alpha \varsigma_{\alpha}(x) \{ 1 - \varsigma_{\alpha}(x) \} \\
\normalsize \varsigma ''_{\alpha}(x) = \alpha^{2} \varsigma_{\alpha}(x) \{ 1- \varsigma_{\alpha}(x) \} \{ 1 - 2 \varsigma_{\alpha}(x) \} \\
\)

Related links

Softmax function

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