Optimization Methods

In the subproblems presented below derive the analytic expression of the requested objects.
After that, implement Python functions to compute considered mathematical functions with JAX1
and compare speed of gradient computations by autodiff approach and by implementation of
analytic expressions that you derived. Jupyter Notebook with such comparison should be also
included in your submission. Consider different dimensions and conclude what approach (autodiff
vs. analytic expression) is asymptotically faster.