# Finding the nth derivative

by christen1289
Tags: derivative
 P: 5 1. The problem statement, all variables and given/known data Find the formula for the nth derivative of the equation f(x)= 1/(1-x)^2 2. Relevant equations 3. The attempt at a solution I have no idea how to attempt this problem. I've tried finding derivatives in order to find a pattern but I can't seem to come up with a pattern that would help me to find a formula
HW Helper
P: 1,662
 Quote by christen1289 1. The problem statement, all variables and given/known data Find the formula for the nth derivative of the equation f(x)= 1/(1-x)^2 3. The attempt at a solution I have no idea how to attempt this problem. I've tried finding derivatives in order to find a pattern but I can't seem to come up with a pattern that would help me to find a formula
Let's start by listing the derivatives you've found. To make this easier to deal with, you could write the function as

f(x) = (1-x)^(-2) and use the Chain Rule. What is f'(x)?
 P: 5 f'(x)=2(1-x)^-3
 P: 980 Finding the nth derivative Can you write that in terms of the original f? Does that help when you apply the derivatives again?
 P: 5 By finding up to the fourth derivative I came up with this formula: nth deriv of f= (n+1)(n!)(1-x)^-(n+2)
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P: 1,662
 Quote by christen1289 By finding up to the fourth derivative I came up with this formula: nth deriv of f= (n+1)(n!)(1-x)^-(n+2)
Yes! (I had to revise something I was going to say: the (-1) factor from the Chain Rule keeps canceling the minus sign from the exponent-factor, so this does stay positive.)

The one further simplification you can make is that (n+1) · (n!) = (n+1)!

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