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Math Help - more implict diff.

  1. #1
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    more implict diff.

    Ok, I don't know how to go about this one at all.

    Find dy/dx by implicit differentiation.
    e^(x/y) = 8x - y
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  2. #2
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    Quote Originally Posted by kwivo View Post
    Find dy/dx by implicit differentiation.
    e^(x/y) = 8x - y
    \left(\frac xy\right)'\cdot e^{x/y}=8-y'

    Find y'
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  3. #3
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    I got dy/dx= ye^(x/y) + 8y^2/ xe^(x/y) + y^2

    Is that right because the hw prog is telling me it's wrong. Maybe I didn't simplify it all the way yet?
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  4. #4
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    Quote Originally Posted by kwivo View Post
    Ok, I don't know how to go about this one at all.

    Find dy/dx by implicit differentiation.
    e^(x/y) = 8x - y
    Quote Originally Posted by Krizalid View Post
    \left(\frac xy\right)'\cdot e^{x/y}=8-y'

    Find y'
    Quote Originally Posted by kwivo View Post
    I got dy/dx= ye^(x/y) + 8y^2/ xe^(x/y) + y^2

    Is that right because the hw prog is telling me it's wrong. Maybe I didn't simplify it all the way yet?
    \frac{d}{dx} \frac{x}{y} = \frac{1 \cdot y - xy^{\prime}}{y^2}

    So from Krizalid's post:
    \left ( \frac{y - xy^{\prime}}{y^2} \right ) \cdot e^{x/y}=8-y^{\prime}

    y e^{x/y} - xy^{\prime}e^{x/y} =  8y^2 - y^2y^{\prime}

    y^2y^{\prime} - xy^{\prime}e^{x/y} =  8y^2 - y e^{x/y}

    (y^2 - xe^{x/y})y^{\prime} =  8y^2 - y e^{x/y}

    y^{\prime} =  \frac{8y^2 - y e^{x/y}}{y^2 - xe^{x/y}}

    (And you really need to use parenthesis!)

    -Dan
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