Please, do this exercise in Python. Plot both the discretized derivatives and the analytic derivative on a single graph. Don't forget to label the axes and the

legend explaining what each line is$.$

Then, compare the results with the exact solution by calculating the maximum error $($i$.$e$.,$ the maximum of the absolute

error$)$ and answer How does the maximum error change with the order of scheme precision? Graph the maximum error

$(y-$axis$)$ as a function of the order of scheme precision $($x$-$axis$).($Hint: You can use the order of scheme precision $($c$)$ is $3,$

but show how extra if it is proved mathematically$).$