Sigmoid Gradient

Problem Statement

Compute the derivative of the Sigmoid function given the activation output.

Background

The Sigmoid function is defined as: $\sigma(z) = \frac{1}{1 + e^{-z}}$

A useful property is that its derivative can be computed directly from the output:

• If $g = \sigma(z)$, then the derivative $g'(z) = g \times (1 - g)$

This makes backpropagation efficient since we already have the sigmoid output from the forward pass.

Your Task

Write a function sigmoid_derivative(sigmoid_output) that returns the gradient values for each element.

Output Format

Return a list of floats representing the derivatives. Round each value to 4 decimal places.