Nth derivative of a function

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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?
 

Answers and Replies

  • #2
Stephen Tashi
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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?
 
  • #3
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Yes its stated properly. I realized I must have misunderstood it and did not approach that the right way
 
  • #4
Stephen Tashi
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Are you only supposed to discover the formula or must you prove the formula that you discover by using induction?
 
  • #5
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It just says find the nth derivative so I assume just find the formula.
 
  • #6
gb7nash
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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.
 
  • #7
Stephen Tashi
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Perhaps, you can utilize

[tex] \frac{1}{1- x} = 1 + x + x^2 + x^3 + x^4 + .... [/tex]
 

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