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Math Help - Simple implicit differentiation, not so simple for me..

  1. #1
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    Simple implicit differentiation, not so simple for me..

    I need help with finding dy/dx by implicit differentiation with this problem:

    x^2y+y^2x=-2

    I am really trying to get this but I am stressing terribly because I don't know how. Turns out, my AP calculus teacher doesn't know how to teach correctly all the time, this leaving me confused a lot.
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    Quote Originally Posted by thatonegurl View Post
    I need help with finding dy/dx by implicit differentiation with this problem:

    x^2y+y^2x=-2

    I am really trying to get this but I am stressing terribly because I don't know how. Turns out, my AP calculus teacher doesn't know how to teach correctly all the time, this leaving me confused a lot.
    To differentiate this you have to use a combination of the product rule and the chain rule. Start with the x^2y term, and work left to right.

    Product rule:

    \frac{d}{dx}(x^2y)=y\frac{d}{dx}x^2+x^2\frac{d}{dx  }(y)

    =2xy+x^2\frac{dy}{dx}

    Did that make sense? Now the next term

    \frac{d}{dx}(y^2x)=y^2\frac{dx}{dx}+x\frac{d}{dx}y  ^2

    =y^2+2xy\frac{dy}{dx}

    Do you see how I applied the chain rule to find \frac{d}{dx}y^2 ?

    So after differentiating the entire equation x^2y+y^2x=-2, we should have:

    2xy+x^2\frac{dy}{dx}+y^2+2xy\frac{dy}{dx}=0

    Now just solve for \frac{dy}{dx}. It's just algebra from here.
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  3. #3
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    Quote Originally Posted by thatonegurl View Post
    I need help with finding dy/dx by implicit differentiation with this problem:

    x^2y+y^2x=-2

    I am really trying to get this but I am stressing terribly because I don't know how. Turns out, my AP calculus teacher doesn't know how to teach correctly all the time, this leaving me confused a lot.
    product rule ... two times

    \frac{d}{dx}(x^2y + y^2x = -2)

    x^2 \cdot \frac{dy}{dx} + y \cdot 2x + y^2 \cdot 1 + x \cdot 2y \cdot \frac{dy}{dx} = 0

    finish up and solve for \frac{dy}{dx}
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