Do this using anonymous functions so that you can easily evaluate $f$ and fprime for any desired value of $x.$

$2.$ Set the initial guess for the root $(x)$ equal to the user input to the function. This is the first value of $x_{\text{o}\text{l}\text{d}}.$

$3.$ Use the formula above to compute $x$ and $x_{\text{n}\text{e}\text{w}}.$

$4.$ Repeat step $3$ until $|x|{10}^{-8}.$ This is a reasonable condition for terminating the loop because it means there isn't much change between successive guesses of the root. Note that on successive loops, $x_{\text{n}\text{e}\text{w}}$ from the previous loop should become $x_{\text{o}\text{l}\text{d}}$ for the current loop. You can do this by defining a single variable $x$ and setting up your algorithm properly.

function should have two inputs:

The first input is the initial guess of the root.

The second input is the variable a$,$ for defining $f(x)=ax-cos(x)$ and $f^{\text{'}}(x)$ within the function.

funfition should have two outputs:

The first output is the value of the root.

The second output is the number of iterations required to find the root. For example, if your loop only runs once, the numer of iterations is $1.$