Need Help finding Derivative (full explanation)

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    Derivative Explanation
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SUMMARY

The discussion focuses on finding the first and second derivatives of the function F(x) = 5/(x^2 - 9). The first derivative, calculated using the Chain Rule, is F'(x) = -10x/(x^2 - 9)^2. The second derivative is derived as F''(x) = (-10(x^2 - 9)^2 + 10x(2(x^2 - 9)2x))/(x^2 - 9)^4. Additionally, the discussion addresses identifying vertical and horizontal asymptotes for the function.

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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

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

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