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Math Help - Implicit Differentiation

  1. #1
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    Implicit Differentiation

    Hi everyone, quick question

    Find dy/dx by differentiating implicitly and calculate its value with x=5, y=1

    (x^2)-(xy^3)=20

    This is what I did:


    2x-3xy(dy/dx)=0
    -3xy(dy/dx)=-2x
    (-2x)/(-3xy)=dy/dx
    2xy/3xy=dy/dx
    2(5)/3(5)(1)=dy/dx
    10/15=dy/dx
    2/3=dy/dx

    That answer is wrong. Where am I making the mistakes?

    Thank you. Much appreciated.
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  2. #2
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    Pittsburgh, PA
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    Quote Originally Posted by Jea9 View Post
    Hi everyone, quick question

    Find dy/dx by differentiating implicitly and calculate its value with x=5, y=1

    (x^2)-(xy^3)=20

    This is what I did:


    2x-3xy(dy/dx)=0


    That answer is wrong. Where am I making the mistakes?

    Thank you. Much appreciated.
    You made your mistake in the first step, unfortunately. You need to differentiate that as a product rule; you can't just differentiate it as if x were a constant. I'm gonna change things around, so it's a little bit easier. Hopefully this doesn't confuse you...

    Differentiating implicitly, you should get 2x=3y^2xdy+y^3dx
    You're trying to isolate dy, so you can rearrange the equation so it reads as follows:
    \frac{2x-y^3}{3xy^2}=dy

    Solve using the point you're given, and you should get dy=\frac{3}{5}

    Hopefully, that is the answer you were looking for?
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  3. #3
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    Thank you!
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