Finding Power Series Representation of Derivatives: 1/x-9

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SUMMARY

The discussion focuses on finding the power series representation of the derivative of the function \( \frac{1}{x-9} \). The correct approach involves rewriting the function as \( -\frac{1}{9} \cdot \frac{d}{dx} \left( \frac{1}{1 - \frac{x}{9}} \right) \), which allows the use of the geometric series expansion. To achieve an accurate representation, one must compute the derivatives of the function up to the desired order and apply the Taylor series formula centered at a suitable point.

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sportlover36
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how can i find a power series representaion of d/dx (1/x-9)
 
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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" .
 
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sportlover36 said:
how can i find a power series representaion of d/dx (1/x-9)
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
 
sportlover36 said:
how can i find a power series representaion of d/dx (1/x-9)

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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