QUESTION $2$

Sharviin and Prakash, while exploring light properties, stumbled upon a dataset depicting the modulation coefficient variations across various wavelengths. Their debate ignited around deciphering the rate of change of modulation coefficients i$.$e$.,\frac{d\text{M}\text{o}\text{d}\text{u}\text{l}\text{a}\text{t}\text{i}\text{o}\text{n}}{d}.$ By using high$-$accuracy numerical differentiation formulas $($backward$,$ centered, and forward$),$ help Sharviin and Prakash to uncover the rate of change of modulation coefficients at the wavelength of $=0\mathrm{.}55.$

Table Q$2$: Modulation Coefficient based on different wavelength.

$\backslash$table$[[$Wavelength$,0\mathrm{.}40,0\mathrm{.}45,0\mathrm{.}50,0\mathrm{.}55,0\mathrm{.}60,0\mathrm{.}65,0\mathrm{.}70],[\backslash$table$[[$Modulation$],[$Coefficient$]],0\mathrm{.}30,0\mathrm{.}32,0\mathrm{.}45,0\mathrm{.}52,0\mathrm{.}48,0\mathrm{.}40,0\mathrm{.}53]]$