x = f(w.x) 1. Consider a network with three inputs x1, x2, x3 as depicted in...

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x = f(w.x) 1. Consider a network with three inputs x1, x2, x3 as depicted in Figure 1. (a) Find the general formula for the 3 first partial derivatives of z with respect to the inputs x. (b) Give the general formula for the total differential of z. (Note: I don't want the definition of a total differential.) (c) Consider the differentiable activation function given by f(y) = y/1+ y and the weight vector w = (2, -2, 1). What are the first partial derivatives of z with respect to each x. (d) Say that there is some error in the inputs to the perceptron in part (c) given by Ax = (Ax1, Ax2, Ax3): (0.01, 0.005, 0.01). Find the approximate error in the output z when x = (3, -3, -1/2), x = (3, 3, -1/2), and x = (-3, 3, -1/2). For which point(s) is z the most sensitive to error in its inputs? = x = f(w.x) 1. Consider a network with three inputs x1, x2, x3 as depicted in Figure 1. (a) Find the general formula for the 3 first partial derivatives of z with respect to the inputs x. (b) Give the general formula for the total differential of z. (Note: I don't want the definition of a total differential.) (c) Consider the differentiable activation function given by f(y) = y/1+ y and the weight vector w = (2, -2, 1). What are the first partial derivatives of z with respect to each x. (d) Say that there is some error in the inputs to the perceptron in part (c) given by Ax = (Ax1, Ax2, Ax3): (0.01, 0.005, 0.01). Find the approximate error in the output z when x = (3, -3, -1/2), x = (3, 3, -1/2), and x = (-3, 3, -1/2). For which point(s) is z the most sensitive to error in its inputs? =