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Math Help - help with implicit differentiation

  1. #1
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    help with implicit differentiation

    sin(xy)=e^xy

    should i use product or chain rule on the left side of the equation? I just started doing these and I am a bit confused. Thanks for any help
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  2. #2
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    Like an onion, you must peel back the layers, working from the outside in. That means chain rule first, with a product rule inside. On the RHS, is it (e^x)y or e^(xy)? You want to be explicit with parentheses.
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  3. #3
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by Ackbeet View Post
    Like an onion, you must peel back the layers, working from the outside in. That means chain rule first, with a product rule inside. On the RHS, is it (e^x)y or e^(xy)? You want to be explicit with parentheses.
    For the left hand side may I ask Ackbeet: are you assuming that y is a function of x in order to use both the chain rule and product rule when differentiating wrt x?

    I would have just use the chain rule and treat y as constant...? I mean having z=f(xy) doesnt mean that y is a function of x right?
    Last edited by bugatti79; April 26th 2011 at 04:44 AM. Reason: Clarification
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  4. #4
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    The title is the clue bugatti.

    Assuming you mean e^(xy), then you want d/dx(xy)*e^(xy).
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    Quote Originally Posted by poirot View Post
    The title is the clue bugatti.

    Assuming you mean e^(xy), then you want d/dx(xy)*e^(xy).
    Indeed. Whenever I see the phrase "implicit differentiation", I assume that we're considering one variable to be a function of the other.
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  6. #6
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by poirot View Post
    The title is the clue bugatti.

    Assuming you mean e^(xy), then you want d/dx(xy)*e^(xy).
    No I was referring to sin (xy) but thanks anyway!
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  7. #7
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    Quote Originally Posted by jimbowickersmack View Post
    sin(xy)=e^xy

    should i use product or chain rule on the left side of the equation? I just started doing these and I am a bit confused. Thanks for any help
    BOTH. Use the chain rule write d sin(xy)/dx= cos(xy) d(xy)/dx, then use the product rule to find d(xy)/dx.
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