Can you help me? it's about numerical numbers question.

First Derivative Error f'(x) = J(+1) - f(x-1) 2h O (h ] ) f ( x) = 1(+2)+ 8f(x,+1) - 8f(x,_1)+f(x 2) 12h o (h* ) Second Derivative f" ( x) = J (*+1) - 2f(x) +f(x_1) O(h) h2 f" ( x ) = f ( * +2 ) + 1of ( x,+1) - 30f( x) + 1of(x,_1)-f(x, 2) 12h2 O(h* ) Third Derivative f" (x) = J(2142) - 2f(x, 1 ) + 2f(x,_1) -f(x, 2) 2h f" ( x ) = f(3) + 8f (x+2) - 13f (x,+1 ) + 13f (x,_1) - 8f(x,_2) + f (x 3) o (h * ) 8h3 Fourth Derivative f (x) = J(*+2) - 4f(x +1) + of(x) - 4f(x,_1) +f(x, 2) O(h? ) ht f" (x) = f(1+3) + 12f(x1+2) + 39f(x,+1) + 56f(x)-39f(x,_,)+12f(x, 2)+f(x-2) o (h * ) In the above table, the formulations to calculate different order derivatives of a function are given by using the central difference method For the function f (x) = In (x), obtain the first, second, third and fourth order derivatives of this function by using the above methods for the neighborhood step h = 0.01 at the point x = 4.0. Soru cozum formati olusturmasi adina birinci turevin elde edilme yontemi asagida verilmistir f (x) = In (x) f (4.0) =? f -(4.0) =? f"(4.0) =? f"(4.0) =? h= 0.01 icin x; = 4.00 *,41 = 4.01 x,_1 = 3.99 x,+2 = 4.02 x,-2 = 3.98 iki nokta icin birinci turev f '(4.0) = J (4.01)-f (3.99) 1.3888-1.3838 - =0.25 2(0.01) 0.02 Dort nokta icin birinci turev f'(4.0) = J (4.02)+8f(4.01)-8f (3.99) + f(3.98) (-1.3913)+8(1.3888)-8(1.3838)+1.3813 12 (0.01) =0.25 12(0.01) Analitik cozum f (x) = In(x) - f'(x)=1/x -> f'(4.0)=0.25 Using the solution format given above, obtain the second, third and fourth order derivatives of the function f (x) = In (x). Compare the results you get with the numerical solution with the derivatives you get with the analytical solution for the relevant function