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Math Help - Learning how to apply the Chain Rule

  1. #1
    Math Engineering Student
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    Learning how to apply the Chain Rule

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    Quote Originally Posted by Krizalid View Post
    For why?
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    Quote Originally Posted by Krizalid View Post
    That's a nice clip! Perhaps anyone who is helped by it (especially the bit where we circle the function to help emphasise inner or outer) will also be interested in this kind of thing...





    ... where straight continuous lines differentiate (downwards) with respect to x, and the dashed line with respect to the dashed balloon expression - so that the triangular network satisfies the rule.

    E.g.,





    We can use the same approach to integrate - just building up the picture from the bottom end instead of the top. (See Balloon Calculus: worked examples from past papers and my other posts to see the process.) E.g.,





    "Don't integrate - balloontegrate!"
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Krizalid View Post
    Nice, but if you make a calculus tutorial you should probably learn to say "differentiate" instead of "derive"
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  5. #5
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    Haha, yeah, I do prefer the word "differentiate."

    To Mush: it's just for people which is about to learn how to apply the chain rule well.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Just out of curiosity is "derive" even techically correct terminology?
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    Quote Originally Posted by Mathstud28 View Post
    Just out of curiosity is "derive" even techically correct terminology?
    I don't think so.

    I don't think the terms, as applied to calculus, are analogous to their normal meanings.

    It's simply defined that:
    A derivative is the rate of change of a function.
    The process of finding a derivative is differentiation.
    The result of n differentiations is the nth derivative, or nth differential of a function.
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