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Math Help - Implicit Differentiation

  1. #1
    Junior Member shepherdm1270's Avatar
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    Implicit Differentiation

    If you could show me the steps as well, that would be great. I'm totally lost:

    find dy/dx

    a) x^2 y^2 = x^3-5y

    b) x^4 + 3 x^2 y^3 - y^2 = 5

    c) x^3 - 6y^2 = 10


    thanks so much for your help
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Yuma, AZ, USA
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    part c

    I'll work out the last one yeah here we go!

    x^3 - 6y^2 = 10<br /> <br />

    The Key point here is that y=f(x) and that we need to use the chain rule for the derivative.

    \frac{d}{dx}x^3 - \frac{d}{dx}6y^2 = \frac{d}{dx}10

    so taking the derivative we get...

    3x^2-12y \cdot \frac{dy}{dx}=0 using the chain rule becuase y is a functin of x.

    now we solve for the derivative

    12y \cdot\frac{dy}{dx}=3x^2 \iff \frac{dy}{dx}=\frac{3x^2}{12}y=\frac{x^2}{4y}
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