Let y(t) = dx(t)/dt, where x(t) = 4cos(2t), < t < . Find y(t) analytically

Let y(t) = dx(t)/dt, where x(t) = 4cos(2πt), − ∞ < t < ∞. Find y(t) analytically and determine a value of T_s for which ∆[x(nT_s)]/T_s = y(nT_s)(consider as possible values T_s = 0.01 and T_s = 0.1). Use the MATLAB function dif for create your own to compute the finite difference. Plot the finite difference in the range [0,1] and compare it with the actual derivative y(t) in that range. Explain your results for the given values of T_s.