2. Consider next an extended network like the one depicted below, where the variables m1, 332, m3 are now governed by space and time by $1- : g1;(.s,t) as depicted in Figure 2. (a) Find the general formula for the 2 rst partial derivatives of z with respect to the inputs .5 and t. (b) Give the general formula for the total differential of z. (c) Using the same activation function and weight vector as in question 1, let the gl(s,t) : 3t, gg(s,t) : s t, and 93(3, t) : 32 + t2. What are the rst partial derivatives of z with respect to s and t. ((1) Say that there is some error in the inputs to the perceptron in part (c) given by As 2 $0.01 and At : $0.05. Find the approximate error in the output 2 when (at) = (1,1) and (s,t) = (2, 2). Weights Activation ml Function : @jk' f(-) @ Inputs Summation Output Figure 2: Extended perceptron