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Math Help - notation question

  1. #1
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    notation question

    Hello

    I am getting a little confused with the notation used in books. Especially when something has already been differentiated or if I need to find the derivative. What is the proper notation that separates the two?

    i.e if you differentiated something how would you write it to show that the operation has already been carried out Vs showing a term that you need to find the derivative of. If that make sense?

    Most of what i have seen is Leibniz's notation.
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  2. #2
    Super Member craig's Avatar
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    Let's have a basic function such as y = x^2.

    The way you would denote differentiation is \frac{dy}{dx} = 2x.

    The \frac{dy}{dx} means the differential of y with respect to x.

    Another way this may be written is \frac{d}{dx}(x^2) = 2x. This is essentially the same, meaning the differential of x^2 with respect to x.

    Does this help at all? Just post back if I've got the wrong idea about what you're asking
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  3. #3
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    Quote Originally Posted by craig View Post
    Let's have a basic function such as y = x^2.
    So how would you write mathematically that you need to differentiate the above without writing the question in English, how would you use the operator? for example i know 2 x 2 needs multiplication because the multiplication operator is there what could you put into the above in terms of notation to say this needs to be differentiated? I hope you see what I am getting at?

    The way you would denote differentiation is \frac{dy}{dx} = 2x.

    The \frac{dy}{dx} means the differential of y with respect to x.
    This shows that differentiation has taken place and how I see most answers.

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

    The above is closer to what i am asking because it explains both before and after. I suppose you could just write the left-hand side as the question.
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  4. #4
    A Plied Mathematician
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    Right. The symbol

    \dfrac{d}{dx}

    is the operator that tells you you need to do something (in this case, differentiate). If, on the other hand, you have a symbol like

    \dfrac{dy}{dx},

    then the operator has already "hit" everything it's supposed to. So in the expression

    \dfrac{d}{dx}\,y+x,

    the operator operates only on the y, whereas in the expression

    \dfrac{d}{dx}(y+x), the derivative operator hits the entire expression y+x.

    In general, the differentiation operator hits everything up to but not including the next addition or subtraction symbol.

    Does that help?
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  5. #5
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    Yes thank you to the both of you this is now much clearer.

    I thought this was correct ,however, none of the books I have that explain the basics of this never explained the operator in any real detail and expected one to take it for granted.
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  6. #6
    A Plied Mathematician
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    You're welcome for whatever I contributed. Have a good one!
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