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Thread: 2.6.5 implicit

  1. MHB Master
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    #1
    $\tiny{166.2.6.5}$
    Find y'
    $$x^2-4xy+y^2=4$$
    dy/dx
    $$2x-4(y+xy')+2yy'=2x-4y-4xy'+2yy'=0$$
    factor
    $$y'(-4x+2y)=-2x+4y=$$
    isolate
    $$y'=\dfrac{-2x+4y}{-4x+2y}
    =\dfrac{-x+2y}{-2x+y}$$

    typo maybe not sure if sure if factoring out 4 helped
    Last edited by karush; March 26th, 2020 at 19:15.

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    #2
    Quote Originally Posted by karush View Post
    $\tiny{166.2.6.5}$
    Find y'
    $$x^2-4xy+y^2=4$$
    dy/dx
    $$2x-4(y+xy')+2yy'=2x-4y-4xy'+2yy'=0$$
    factor
    $$y'(-4x+2y)=-2x+4y=$$
    isolate
    $$y'=\dfrac{-2x+4y}{-4x+2y}
    =\dfrac{-x+2y}{-2x+y}$

    typo maybe not sure if sure if factoring out 4 helped
    What you've done is correct.

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