MATLAB Code for this: In the class, we showed that the first$-$order derivative of a function, $P,$ with respect to the

independent variable, $x,$ can be approximately calculated using the forward difference:

$\frac{dP}{dx}$~~$\frac{P(x+x)-P(x)}{x}$

We also used the Taylor series to show that the forward difference approximation has a

first$-$order accuracy, $O(x),$ which means that its truncation error is proportional to the value

of $x.$

Note that the backward finite difference approximation is written as:

$\frac{\text{d}\text{e}\text{l}\text{p}}{\text{d}\text{e}\text{l}\text{x}}(x)=\frac{P(x)-P(x-x)}{x}$

Please also use the Taylor series method to prove that the backward finite difference has a

first$-$order accuracy, $O(x).$