Given definition of Newton's Method: see image or last section of my question

HW problem: Use Newton's Method to approximate $\sqrt[4]{2}by$ solving the equation $x^4-2=0.$ Start with $x_0=1,$ and find $x_2.$ Give your answer $as$ a rational number.

Side note: Before every step, please write a generalization $of$ what that step $is$ about $(thisisso$ I can apply the steps $to$ other questions$).$

Given def of Newton's Method: Let $f$ be a differentiable function on an interval I with a root in I. To approximate the value of the root, accurate to $d$ decimal places:

$1.$ Choose a value $x_0$ as an initial approximation of the root. $($This is often done by looking at a graph of $f.)$

$2.$ Create successive approximations iteratively; given an approximation $x_n,$ compute the next approximation $x_{n+1}$ as $x_{n+1}=x_n-\frac{f(x_n)}{f\text{'}(x_n)}.$

$3.$ Stop the iterations when successive approximations do not differ in the first $d$ places after the decimal point.