Tanh

The hyperbolic tangent activation function is given by

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

and its derivative is

$$\frac{dg}{dx} = 1 - \left(\frac{e^x - e^{-x}}{e^x + e^{-x}} \right)^2 = 1 - g(x)^2$$

This activation function has a similar shape as the logisitc function except that its domain definition is centered on 0. It also has a steeper derivative at $x=0$. This activation function is usually used with hidden layers and is a relatively common choice.