In this problem we mainly focus on properties of the sigmoid function (x)=1+ex1. 1. (5 points) Show that (x)+(x)=1. 2. (10 points) Show that dxd(x)=(x)(1(x)). 3. (10 points) The sigmoid function is often used to constrain the input into the range (0,1). There are other constraining functions, one of which is the tanh function tanh(x)=ex+exexex Tanh function squashes the input xR into (1,1), which is more suitable if we want the output range to be symmetric around 0 . Show that tanh(x)=2(2x)1