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Math Help - use explicit differentiation to find y prime (simple)

  1. #1
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    use explicit differentiation to find y prime (simple)

     y = sin(3x+4y)
     y' = cos(3x+4y)(3+4y')
     \frac{y'}{3+4y'} = cos(3x+4y)

    //please help me finish
    Last edited by rabert1; April 25th 2012 at 07:04 PM.
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  2. #2
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    Re: use explicit differentiation to find y prime (simple)

    Hello, rabert1!

    y \:=\: \sin(3x+4y)

    y' \:=\: \cos(3x+4y)\cdot (3+4y')

    We have: . . . . . . y' \;=\;(3+4y')\cos(3x+4y)

    n . . . . . . . . . . . . y' \;=\;3\cos(3x+4y) + 4y'\cos(3x+4y)

    . . . y' - 4y'\cis(3x+4y) \;=\;3\cos(3x+4y) . .
    Get the y' terms on one side.

    y'\big[1 - 4\cos(3x+4y)\big] \;=\;3\cos(3x+4y) . .
    Factor.

    w . . . . . . . . . . . . y' \;=\;\frac{3\cos(3x+4y)}{1 - 4\cos(3x+4y)}
    Thanks from rabert1
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