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Math Help - More differentiation problems

  1. #1
    Super Member Showcase_22's Avatar
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    More differentiation problems

    I solved a few more differentiation problems, but got stuck on the following questions:

    Find an expression in tems of x and y for dy/dx, given that:

    (x-y)^4=x+y+5

    and

    ((xy)^0.5)+x+y^2=0
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  2. #2
    Forum Admin topsquark's Avatar
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    The Captain got it right, I goofed!

    -Dan
    Last edited by topsquark; September 8th 2006 at 06:20 AM. Reason: Made an oopsy!
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Showcase_22
    I solved a few more differentiation problems, but got stuck on the following questions:

    Find an expression in tems of x and y for dy/dx, given that:

    (x-y)^4=x+y+5
    Implicit differentiation should be your watchword.

    <br />
\frac{d}{dx}(x-y)^4=\frac{d}{dx}(x+y+5)<br />

    so:

    <br />
4(x-y)^3 \left(1-\frac{dy}{dx}\right)=1+\frac{dy}{dx}<br />
.

    Now rearrange into the required form.

    RonL
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Showcase_22
    \sqrt{xy}+x+y^2=0
    \left ( \frac{1}{2} \frac{1}{\sqrt{xy}} \right ) \cdot \left ( y + x \frac{dy}{dx} \right ) + 1 + 2y \frac{dy}{dx} = 0
    where the first set of parenthesis is the \frac{df}{dg} and the second set is the \frac{dg}{dx}.

    All that's left is to solve for \frac{dy}{dx}. I leave it to you. Please feel free to post if you have any difficulties with it.

    -Dan
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by topsquark
    Again, this is a problem in implicit differentiation.

    Recall the chain rule:
    \frac{d}{dx}f(g(x)) = \frac{df}{dg} \frac{dg}{dx}

    So the LHS of your problem becomes, upon differentiation:
    4(x - y)^3 \cdot - \frac{dy}{dx}

    ?

    RonL
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by CaptainBlack
    ?

    RonL
    I saw what I did (or didn't do) when I caught your post. Ah well, it's been a morning already!

    -Dan
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