Refer to the neural networks on page 7 of the Neural Networks slides, there are three layers (input layer, hidden layer, and output layer). • Q9.1 Compute the derivative of hyperbolic tangent tanh(x) = (e² −e¯³)/(e² +e¯*), express the derivative in terms of the original function. ⚫ Q9.2 Replace the sigmoid function in the neural networks with tanh function. Calculate the derivative ǝJ/Owij where wij is a parameter connecting i-th node in the hidden layer and j-th node in the output layer (assume the output for i-th node in the hidden layer is ui, the output and label for j-th node in the output layer are o; and yj, respectively). Write the optimization problem with constraint as the Lagrangian form, and solve it: minimize f(x, y) = x² + 2y² - 2 x.y subject to h(x, y) = x+y-1=0

Refer to the neural networks on page 7 of the Neural Networks slides, there are three layers (input layer, hidden layer, and output layer). • Q9.1 Compute the derivative of hyperbolic tangent tanh(x) = (e² −e¯³)/(e² +e¯*), express the derivative in terms of the original function. ⚫ Q9.2 Replace the sigmoid function in the neural networks with tanh function. Calculate the derivative ǝJ/Owij where wij is a parameter connecting i-th node in the hidden layer and j-th node in the output layer (assume the output for i-th node in the hidden layer is ui, the output and label for j-th node in the output layer are o; and yj, respectively). Write the optimization problem with constraint as the Lagrangian form, and solve it: minimize f(x, y) = x² + 2y² - 2 x.y subject to h(x, y) = x+y-1=0