tanh(x) activation function is widely used in neural networks. In this tutorial, we will discuss some features on it and disucss why we use it in nerual networks.

## tanh(x)

tanh(x) is defined as:

The graph of tanh(x) likes:

We can find:

tanh(1) = 0.761594156

tanh(1.5) = 0.905148254

tanh(2) = 0.96402758

tanh(3) = 0.995054754

## The feature of tanh(x)

tanh(x) contains some important features, they are:

- tanh(x)∈[-1,1]
- nonlinear function, derivative

## tanh(x) derivative

The derivative is:

tanh(x)’ = 1-(tanh(x))^{2}

The graph looks like:

## Why should we use tanh(x) in neural networks?

There are two main reasons:

- tanh(x) can limit the value in [-1, 1]
- tanh(x) can convert a linear function to nonlinear, meanwhile it is derivative.

## Useful Equations

\[tanh(x+y)=\frac{tanh(x)+tanh(y)}{1+tanh(x)tanh(y)} \]

\[tanh(x-y)=\frac{tanh(x)-tanh(y)}{1-tanh(x)tanh(y)} \]

\[tanh(2x)=\frac{2tanh(x)}{1+tanh^2(x)}\]