1. What is the Tanh Function?

The tanh (hyperbolic tangent) function is a mathematical function that relates the hyperbolic sine and cosine functions. It's similar to the regular tangent function but for hyperbolic angles.

2. How Does the Calculator Work?

The calculator uses the tanh equation:

Where:

• \( x \) — Input value (dimensionless)
• \( e \) — Euler's number (~2.71828)

Explanation: The function calculates the ratio of the difference to the sum of exponential functions with positive and negative arguments.

3. Applications of Tanh

Details: The tanh function is widely used in physics, engineering, and machine learning (as an activation function in neural networks). It maps real numbers to the range (-1, 1).

4. Using the Calculator

Tips: Enter any real number value for x. The calculator will return the corresponding tanh value between -1 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of tanh function?
A: The tanh function outputs values between -1 and 1 for all real inputs.

Q2: How does tanh compare to sigmoid?
A: Tanh is similar to sigmoid but ranges from -1 to 1 instead of 0 to 1, making it zero-centered.

Q3: What's the derivative of tanh?
A: The derivative is \( 1 - \tanh^2(x) \), which is useful in backpropagation algorithms.

Q4: What are some special values of tanh?
A: tanh(0) = 0, tanh(∞) = 1, tanh(-∞) = -1

Q5: Why is tanh used in neural networks?
A: Its zero-centered output helps with convergence during training, though ReLU is now more common in hidden layers.