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Math Help - what will this d/dx y^3 be?

  1. #1
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    what will this d/dx y^3 be?

    d/dx y^3 will equal to zero or 3y^2 ?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: what will this d/dx y^3 be?

    If y is a function of x, then you also need to apply the chain rule to get:

    \frac{d}{dx}(y^3)=3y^2\frac{dy}{dx}
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  3. #3
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    Re: what will this d/dx y^3 be?

    this kind of confuses me. if there was a constant instead of y like:
    d/dx 4^3
    it would have been Zero right?

    yes I'm doing implicit differentiation and I don't know what it is though,
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    Re: what will this d/dx y^3 be?

    and what would be
    d/dx y
    just y.
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    MHF Contributor MarkFL's Avatar
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    Re: what will this d/dx y^3 be?

    Yes, if y is a constant, then it would be zero. However, in an implicit relation, it is implied that y depends on x. So, you would use the form in my first post above.
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  6. #6
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    Re: what will this d/dx y^3 be?

    so if they declare y as constant

    this would become zero as well right? d/dx y^3
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    MHF Contributor MarkFL's Avatar
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    Re: what will this d/dx y^3 be?

    Normally you would only treat y as a constant when doing partial differentiation. And you don't know what \frac{dy}{dx} is, this is normally what you are trying to express as a function of x and y.
    Last edited by MarkFL; December 12th 2012 at 08:48 PM.
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  8. #8
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    Re: what will this d/dx y^3 be?

    It depends on whether you are trying to do a total derivative or a partial derivative. If it's a total derivative, use implicit differentiation. If it's a partial derivative, treat y as a constant.
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  9. #9
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    Re: what will this d/dx y^3 be?

    Normally, "y" is used as a variable or function of x. You have been told repeatedly that if y is independent of x, then so is f(y) for any f and so df(y)/dx= 0. If, however, y is itself some function of x, then df(y)/dx= (df/dy)(dy/dx), by the chain rule.
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