TeXipedia

tanh

Represents the hyperbolic tangent function, a fundamental mathematical function that maps real numbers to values between -1 and 1.

Overview

Essential in various mathematical and scientific applications, particularly in neural networks, signal processing, and differential equations.

  • Commonly used in machine learning as an activation function due to its smooth, bounded output range
  • Appears frequently in physics for describing wave mechanics and electromagnetic phenomena
  • Important in engineering applications involving damped oscillations and control systems
  • Serves as a key function in complex analysis and differential geometry

Examples

Hyperbolic tangent function in a basic mathematical expression

tanh(x)=sinh(x)cosh(x)\tanh(x) = \frac{\sinh(x)}{\cosh(x)}
\tanh(x) = \frac{\sinh(x)}{\cosh(x)}

Neural network activation function with specific input

f(x)=tanh(wx+b)f(x) = \tanh(wx + b)
f(x) = \tanh(wx + b)

Solution to a differential equation involving hyperbolic tangent

y(t)=Atanh(ωt)y(t) = A\tanh(\omega t)
y(t) = A\tanh(\omega t)