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Let-f-W-be-a-function-of-vector-W-R-N-i-e-f-W-1-1-e-W-T-x-Determine-the-first-derivative-and-matrix-of-second-derivatives-of-f-with-respect-to-W-




Question Number 203898 by necx122 last updated on 02/Feb/24
Let f(W) be a function of vector W ∈  R^N ,  i.e. f(W) = (1/(1 + e^(−W^T x) ))  Determine the first derivative and  matrix of second derivatives of f with  respect to W
$${Let}\:{f}\left({W}\right)\:{be}\:{a}\:{function}\:{of}\:{vector}\:{W}\:\in\: {R}^{{N}} , \\ $$$${i}.{e}.\:{f}\left({W}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{e}^{−{W}^{{T}} {x}} } \\ $$$${Determine}\:{the}\:{first}\:{derivative}\:{and} \\ $$$${matrix}\:{of}\:{second}\:{derivatives}\:{of}\:{f}\:{with} \\ $$$${respect}\:{to}\:{W} \\ $$$$ \\ $$
Commented by necx122 last updated on 01/Feb/24
This looks like an AI activation function (sigmoid) but I just don't seem to navigate my way through it properly.
Commented by necx122 last updated on 02/Feb/24
Please, can I get help for this

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