Create a function, mynumdiff $(f,x)$ to compute the derivative of the function $f(x)$ where $x$ is the

grid on which $f(x)$ has been computed. Assume $f(x)=sin(x)($Groups I,II$),f(x)=cos(x)($Groups

III,IV$)$ and $f(x)=$exp$(x)($Groups V$,$VI$,$VII$).$ Call mynumdiff $(f,x)$ between the limits of $x$ as $,$

$2$ pi$]$ having grid points equally spaced at a distance dx $.(20$ marks$)$

a$.$ Compute the derivative using the forward difference, backward difference and central

difference formula and plot the analytical derivative on the same graph.

b$.$ Compute the error at each point for different values of dx $($varying by atleast $2$ orders

of magnitude$)$ and plot on a separate log$-$log graph for each difference formula.

c$.$ Plot max error in the entire domain as function of dx for all the three difference

formulae on the same graph. What do you observe?