Hyperbolic Tangent

The hyperbolic tangent (tanh) is a sigmoid function centered at the origin. It has a bounded output range of between -1 and 1.

We can define tanh using the following equation:

$$\text{tanh}(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$$

The derivative of the tanh function is:

$${\text{tanh}}^{\text{'}}(x)=1-{\text{tanh}}^2(x)$$

Computing the hyperbolic tangent in numpy

import numpy as np

print(f"tanh(0) = {np.tanh(0)}")

---

This page references the following sources:

• DeepLearning.AI Deep Learning Specialization (course 1, week 3)
• Wikipedia's "Hyperbolic functions" article
• numpy API reference (tanh)