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Math Help - Implicit Differentiation Problem

  1. #1
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    Implicit Differentiation Problem

    Hi,

    This is the last one before everyone here thinks Im taking liberities!

    Got this expression

    cos y - x^2y^3 + 2y = pi

    and have to put it in the form of f(x,y)

    My understanding is that pi would disappear with it being a constant but I feel this is not right?

    can the middle variables of x and y be sorted by using the product rule?


    Sorry to put loads of posts up at once but Im playing catch up as being a fire fighter is not the best profession to have whilst learning calculus at home!

    Cheers again
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  2. #2
    Eater of Worlds
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    You want to differentiate implicitly?. Yes, you can use the product rule on the middle term.

    You get:

    -sin(y)\frac{dy}{dx}-3x^{2}y^{2}\frac{dy}{dx}-2xy^{3}+2\frac{dy}{dx}=0

    Now, solve for dy/dx.
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  3. #3
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    nice one cheers
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  4. #4
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    does :

    3x^2/cos(y)(2y^2) look right or is that an utter cock up?
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  5. #5
    GAMMA Mathematics
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    Quote Originally Posted by wannberocketscientist View Post
    does :

    3x^2/cos(y)(2y^2) look right or is that an utter cock up?
    Not sure what you did, but going from Galactus' work:

    -sin(y)\frac{dy}{dx}-3x^{2}y^{2}\frac{dy}{dx}-2xy^{3}+2\frac{dy}{dx}=0

    (-sin(y)-3x^{2}y^{2}+2)\frac{dy}{dx}=2xy^{3}

    \frac{dy}{dx}=\frac{2xy^{3}}{-sin(y)-3x^{2}y^{2}+2}
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