in python

A. Use the definition of derivative to write a python function that calculate the siope at 4 for cosx using different values of h,h=[0,5,0,3,0.2,0,1,0.01,0.001]. For each value of h calculate the true error, the relative true error, the approximate error and the relative approximate error. B. with the smallest value of h calculate the derivate for cosx at different points, points =[0,8,6,4,2,]. C. Using matpiotilb to plot the derivatives in part B. D. Prove through the plot that the derivate of cosx is sinx by ploting sinx in the plot of part C and show that sinx passes through all derivate points in part C