Deriving the Cube Root Formula with Newton-Rhapson's Method

[SherlockOhms]

Homework Statement

Derive cube root formula using Newton-Rhapson's method. x - y^3 = 0.

Homework Equations

x_{n + 1} = x_n - f(x_n)/f'(x_n)

The Attempt at a Solution

I know that the solution is (2y + (x/y^2))/3
I tried using implicit differentiation and stuff but I can't get this out. Any tips?

 

[LCKurtz]

Homework Statement

Derive cube root formula using Newton-Rhapson's method. x - y^3 = 0.

Homework Equations

x_{n + 1} = x_n - f(x_n)/f'(x_n)

The Attempt at a Solution

I know that the solution is (2y + (x/y^2))/3
I tried using implicit differentiation and stuff but I can't get this out. Any tips?

I think your use of x and y is confusing you. If you want the cube root of $n$ you might solve $f(x) = x^3 - n$ for its roots using your above formula. No implicit differentiation needed and you can switch the names of the variables at the end if you want to.

 

[SherlockOhms]

I think your use of x and y is confusing you. If you want the cube root of $n$ you might solve $f(x) = x^3 - n$ for its roots using your above formula. No implicit differentiation needed and you can switch the names of the variables at the end if you want to.

So, differentiate "n" as a constant and "x^3" as normal? Thanks for that.