how can i find a power series representaion of d/dx (1/x-9)
You can find an approximation by calculating the Taylor series around some point (a=0 would probably be easiest). All you need to do is find derivatives of the function up to the nth derivative, depending on how accurate you want the representation to be, and substitute them into the general series given http://en.wikipedia.org/wiki/Taylor_series" [Broken].
It looks like you may have some sort of a typo. At x=0, 1/x is infinite.
I mean for it to say d/dx (1/(x-9)) sorrry
This expression can be written as -1/9 * d/dx (1/(1-x/9)). Then think geometric series. Can you see it from there?
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