Simple? maclaurin series (1-x)^-2

[ivan77]

Homework Statement

what is the maclaurin series expansion of the function (1-x)^-2

Homework Equations

maclaurin series

The Attempt at a Solution

part of the solution is to find the n derivatives of the function to setup the series
MY ANSWERS
n fⁿ(x)
0 (1-x)^-2 this should be the 0th derivative of the function
1 -2(1-x)^-3 this should be the first derivative of the function
2 6(1-x)^-4 second derivative
3 -24(1-x)^-5 third derivative
TEXTBOOK ANSWERS
n fⁿ(x)
0 (1-x)^-2 this should be the 0th derivative of the function
1 2(1-x)^-3 this should be the first derivative of the function
2 6(1-x)^-4 second derivative
3 24(1-x)^-5 third derivative
NOTICE the lack of negatives on the 1 and 3 derivative.

The thing that is confusing the heck out of me as well is that when I look for the first derivative of the function (1-x)^-2 on wolfram alpha it gives me -2(1-x)^-3, but when I look for the maclaurin series, the answer does not show the negative sign.

Please help

 

[Dick]

Homework Statement

what is the maclaurin series expansion of the function (1-x)^-2

Homework Equations

maclaurin series

The Attempt at a Solution

part of the solution is to find the n derivatives of the function to setup the series
MY ANSWERS
n fⁿ(x)
0 (1-x)^-2 this should be the 0th derivative of the function
1 -2(1-x)^-3 this should be the first derivative of the function
2 6(1-x)^-4 second derivative
3 -24(1-x)^-5 third derivative
TEXTBOOK ANSWERS
n fⁿ(x)
0 (1-x)^-2 this should be the 0th derivative of the function
1 2(1-x)^-3 this should be the first derivative of the function
2 6(1-x)^-4 second derivative
3 24(1-x)^-5 third derivative
NOTICE the lack of negatives on the 1 and 3 derivative.

The thing that is confusing the heck out of me as well is that when I look for the first derivative of the function (1-x)^-2 on wolfram alpha it gives me -2(1-x)^-3, but when I look for the maclaurin series, the answer does not show the negative sign.

Please help

The book is right. You are forgetting to use the chain rule.

 

[Mark44]

The book is right. You are forgetting to use the chain rule.

And in particular, that d/dx(1 - x) = -1

 

[ivan77]

I feel pretty silly. I very much appreciate the quick responses.