GATE DA 2024 Q33: Derivative of the sigmoid where its value is 0.4

Let $f: \mathbb{R} \to \mathbb{R}$ be the function $f(x) = \dfrac{1}{1+e^{-x}}$ .

The value of the derivative of $f$ at $x$ where $f(x) = 0.4$ is ______ (rounded off to two decimal places).

Note: $\mathbb{R}$ denotes the set of real numbers.

Try it: numerical answer: type the value

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Answer: 0.24 (official GATE 2024 final answer key)

Concept used: Derivative of the sigmoid: $f'(x) = f(x)\,(1 - f(x))$ .

First step: $f'(x) = 0.4 \times 0.6$ .

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key