What is the nth derivative of the function f(x)= x^n/(1-x)?

[jasonbob]

Homework Statement

Find the nth derivative of the function f(x)= x^n/(1-x)

Homework Equations

The Attempt at a Solution

I got nx^n-1*(1-x)-x^n(-1) all over (1-x)^2

Is this correct and if so is their any steps afterwards?

 

[Stephen Tashi]

Find the nth derivative of the function f(x)= x^n/(1-x)

You only found the first derivative. Did you state the problem correctly?

 

[jasonbob]

Yes its stated properly. I realized I must have misunderstood it and did not approach that the right way

 

[Stephen Tashi]

Are you only supposed to discover the formula or must you prove the formula that you discover by using induction?

 

[jasonbob]

It just says find the nth derivative so I assume just find the formula.

 

[gb7nash]

For this type of problem, just take a few derivatives and find the pattern. You'll be able to see what it is after taking 3 or 4 of them.

 

[Stephen Tashi]

Perhaps, you can utilize

\frac{1}{1- x} = 1 + x + x^2 + x^3 + x^4 + ...