Problem 2. Prove the updating equation for backpropagation learning algorithm. You may use the following steps: I Step 1. Show that for the Logistic Activation function for the neurons as below: 1 olv)= 1 + exp(-v) Then the derivative is as following: c'(t) = o(t)(1- o(t)) Step 2. Using the model of a single neuron, calculate the input of the neuron j, net as: (W, X, + Threshold) where X is the activation of previous layer neuron i W, is the weight of going from node i to nodej Dp is the number of neurons in the previous layer Step 3. Using the error function below, E(T) = 20,()1{? ko Step 3. Using the error function below, E(5)= 30; ( 1:())? 2 ** Take the partial derivative with respect to the weight as: OE(*) owa Use chain rule of calculus and simplify it using results of steps 1 and 2, show that: DE(*) =-y, (net) (1- 9(net)) (t, - y) OWjk