How to Find the Second Derivative with Given Equation at a Specific Point?

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SUMMARY

The discussion focuses on finding the second derivative of the equation \((x+2y)\cdot \dfrac{dy}{dx}=2x-y\) at the point (3,0). The first derivative is determined as \(\dfrac{dy}{dx}=\dfrac{2x-y}{x+2y}\). To find \(\dfrac{d^2y}{dx^2}\), participants must apply implicit differentiation to the first derivative. The final value of the second derivative at the specified point is calculated through these steps.

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karush
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If $(x+2y)\cdot \dfrac{dy}{dx}=2x-y$ what is the value of $\dfrac{d^2y}{dx^2}$ at the point (3,0)?
ok not sure of the next step but
$\dfrac{dy}{dx}=\dfrac{2x-y}{x+2y}$
 
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Re: 231 value of second dirivative

See https://mathhelpboards.com/calculus-10/297-ap-calculus-exam-2nd-derivative-26690.html.
 

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