Need Help finding Derivative (full explanation)

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    Derivative Explanation
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Discussion Overview

The discussion revolves around finding the derivatives of the function F(x) = 5/(x^2 - 9), as well as identifying its vertical, horizontal, and slant asymptotes. The scope includes mathematical reasoning and derivative calculations.

Discussion Character

  • Mathematical reasoning, Technical explanation

Main Points Raised

  • Participants seek to find the first and second derivatives of the function F(x) = 5/(x^2 - 9).
  • There is a clarification regarding the correct form of the function, with some participants questioning whether it is 5/(x^2) - 9 or 5/(x^2 - 9).
  • One participant suggests rewriting the function as 5(x^2 - 9)^(-1) to apply the Chain Rule for differentiation.
  • A participant provides the first derivative as -10x/(x^2 - 9)^2 and later updates with the expression for the second derivative.

Areas of Agreement / Disagreement

Participants generally agree on the function being 5/(x^2 - 9), but there are differing views on the steps and methods for finding the derivatives and asymptotes.

Contextual Notes

Some mathematical steps and assumptions in the derivative calculations remain unresolved, particularly regarding the application of the Chain Rule and the simplification of the second derivative.

blakejohnston
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F(x)=5/(x^2)-9

Find F'(x)&F''(x)
Find the Vertical Asymptote, Horizontal, and Slant
 
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blakejohnston said:
F(x)=5/(x^2)-9

Find F'(x)&F''(x)
Find the Vertical Asymptote, Horizontal, and Slant

Is your function $\displaystyle \begin{align*} \frac{5}{x^2} - 9 \end{align*}$ or $\displaystyle \begin{align*} \frac{5}{x^2 - 9} \end{align*}$?
 
The second.
 
Write it as $\displaystyle \begin{align*} 5 \left( x^2 - 9 \right) ^{-1} \end{align*}$ and use the Chain Rule.
 
first derivative: -10x/(x^2-9)^2

- - - Updated - - -

- - - Updated - - -

The second derivative: (-10(x^2-9)^2+10x(2(x^2-9)2x))/(x^2-9)^4
 

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