6. Let L = e'lue'. :17:- = 352an for j = 0111.. .,N 1. Take N = 3. Using yeur H't package obtain PglEI} and nd a speutrel approximation of the derivative of 3\"" at IJ for j = , 1,. _ _ 1N l by oomputing PIJ-II. Compute the actual error in the approximation. 'f. Note that ENE} is again a trigonometric polynomial of degree 5 NEE and whose eoeieients can be computed from those of Haz] via the FFT. {a} 'Write a code to oempute a [apeutra approximatien to- the derivative at 3:1; = jl[21'r;"N} for j = , 1,. . .1N l for the corresponding periodic array 33 j = , 1, __ .1 N 1_~ using one DFT and one im'erse DF'I', i.e. in order Nlog2 N operations. {h} Test your code by comparing with your answer of the previous problem. {c} Dhserve the behavior of the error as N is increased to l, and 32. Note: the contribution to the derivative from the k = NEE node should be zero. Make sure to set the Fourier L'oeiL'ient for k = NE? of the derivative erlual to zero