Compute the derivative ficts of the logistic sigmoid 1 foo. 1 + exp(-x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Title: Calculating the Derivative of the Logistic Sigmoid Function
In this section, we will learn how to compute the derivative of the logistic sigmoid function, which is commonly used in machine learning, particularly in logistic regression and neural networks.
### The Logistic Sigmoid Function
The sigmoid function, denoted as \( f(x) \), is defined as follows:
\[
f(x) = \frac{1}{1 + \exp(-x)}
\]
### Task
Compute the derivative, \( f'(x) \), of the logistic sigmoid function.
### Explanation
The logistic sigmoid function transforms any real-valued number into a value between 0 and 1, making it especially useful for predicting probabilities. Understanding its derivative is crucial for optimization algorithms like gradient descent, which are employed in training models.
The image shows the beginning of a process to find \( f'(x) \), which would involve using the chain rule and other calculus techniques.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dbb4ae4-0d65-4baa-9481-63f79be91eca%2Ff2eb6d35-d1db-4357-9f49-a0eb2dc8b520%2Fneliece_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Calculating the Derivative of the Logistic Sigmoid Function
In this section, we will learn how to compute the derivative of the logistic sigmoid function, which is commonly used in machine learning, particularly in logistic regression and neural networks.
### The Logistic Sigmoid Function
The sigmoid function, denoted as \( f(x) \), is defined as follows:
\[
f(x) = \frac{1}{1 + \exp(-x)}
\]
### Task
Compute the derivative, \( f'(x) \), of the logistic sigmoid function.
### Explanation
The logistic sigmoid function transforms any real-valued number into a value between 0 and 1, making it especially useful for predicting probabilities. Understanding its derivative is crucial for optimization algorithms like gradient descent, which are employed in training models.
The image shows the beginning of a process to find \( f'(x) \), which would involve using the chain rule and other calculus techniques.
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