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Math Help - Slope of a tangent through implicit differentitation

  1. #1
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    Exclamation Slope of a tangent through implicit differentitation

    i have a problem where I have to find tangent line to the curve: 1x24xy+4y3=81
    At the point (71).
    Can anyone help?
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  2. #2
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    Quote Originally Posted by quitie0690 View Post
    i have a problem where I have to find tangent line to the curve: 1x24xy+4y3=81
    At the point (71).
    Can anyone help?
    Is the equation x^2 - 4xy + 4y^3 = 81 ? Have you learned implicit differentiation?
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    Yes that's the line. Sorry about that. Well, let's just say my prof. isn't the best in the world (aka the world's biggest understatement). We've only done a few examples. but I can't figure this one out. Can you help?
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    Quote Originally Posted by mr fantastic View Post
    Is the equation x^2 - 4xy + 4y^3 = 81 ? Have you learned implicit differentiation?
    Quote Originally Posted by quitie0690 View Post
    Yes that's the line. Sorry about that. Well, let's just say my prof. isn't the best in the world (aka the world's biggest understatement). We've only done a few examples. but I can't figure this one out. Can you help?
    Differentiate both sides with rspect to x:

    Use the product rule on 4xy to get 4y + 4x \frac{dy}{dx}.

    Use the chain rule on 4 y^3 to get 12 y^2 \frac{dy}{dx}.

    Now substitute (-7, 1) and make \frac{dy}{dx} the subject.
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