2 Differential Calculus and Optimization Consider the multivariate function NX) : rx a)TA(x a) (2) where A : [:21 El] (3) and 0 a : [2] (4) and answer the following questions. 1. Compute the partial derivatives of the function x) in (2). 2. What is the formal mathematical expression of the gradient of a function? 3. Compute the gradient of the function f (x) in (2). 4. What is the value of the gradient at the point (0.0)? 5. To be solved without programming. Using the gradient descent algorithm, execute a single iteration from a randomly selected point. What is the function's value at the new point after this one iteration? The learning rate can be selected from the range of 0.001 to 0.01. 6. Apply the gradient descent algorithm starting from a randomly selected point and stopping when the norm of the gradient is less than 10'5. What is the interpretation of the nal point that is attained after this process? The learning rate can be selected from the range of 0.001 to 0.01."1 1Note that this question requires some research since we did not go through the Theorem in our lectures. 2For this question Python might be a preferable choice