Numerical methodsWrite a user$-$defined function in MatLab that applies the Ridders interpolation method for

calculating derivatives. The function should be called $[a,df]=$

DerivativeRidders $($func$,x,h,$ err$),$ where a is the Romberg matrix, $df$ is the

derivatrive, func is the function defined with function handle $($@$),x$ is the value at which the

derivative is required, $h$ is the step and err is the error. For the derivative the function should

use the two$-$point central difference scheme. If the err is not defined, the function should select

automatically er $r={10}^{-7}.$ If $h=0,$ the function should show a message $\text{'}h$ must be nonzero'. The

error should be calculated as the maximum value compared with the previous two values $[$e$.$g$.$

for the case of B$1$ the error should be the max$($abs$($B$1-$A$2),$ abs$($B$1-$A$1)),$ see lecture slides$].$

Use also format long in the function so that you see as many digits as possible. The size of

the Romberg matrix should be fixed to number $5.$ The only build$-$in functions of MatLab you

are allowed to use are: nargin, feval, max, abs$,$ disp. After building the function use it to

estimate the derivative of function:

$f(x)=\frac{e^x}{sin(x)-x^2}$

at $x=1,$ with $h=0\mathrm{.}01.$ Report the results and submit with the MatLab files. $(30\%)$