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Math Help - Differentiate fractions

  1. #1
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    Question Differentiate fractions

    Hi

    How would you differentiate the following:

    2x^2 + 2000/r

    I know it would be first 4x + ?UNKNOWN?

    Im not sure how to differenctiate 2000/r
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  2. #2
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    Quote Originally Posted by taurus View Post
    Hi

    How would you differentiate the following:

    2x^2 + 2000/r

    I know it would be first 4x + ?UNKNOWN?

    Im not sure how to differenctiate 2000/r
    Hello,

    that depends:

    a) If your function reads f(x) = 2x^2 + \frac{2000}{r} then r is considered to be a constant.

    b) If your function reads f(r) = 2x^2 + \frac{2000}{r} then x is considered to be a constant.

    c) If your function reads f(t) = 2x^2 + \frac{2000}{r} then x and r are considered to be a constant.

    According to your rematk it seems to be a)
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  3. #3
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    Question

    oh right, could you run through how you would solve each of those then please for my own knowledge?
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  4. #4
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    Quote Originally Posted by earboth View Post
    Hello,

    that depends:

    a) If your function reads f(x) = 2x^2 + \frac{2000}{r} then r is considered to be a constant.

    b) If your function reads f(r) = 2x^2 + \frac{2000}{r} then x is considered to be a constant.

    c) If your function reads f(t) = 2x^2 + \frac{2000}{r} then x and r are considered to be a constant.

    According to your rematk it seems to be a)
    Yes.

    Or, if it is in a case where r is also a variable, and the differentiation is with respect to x, then
    d/dx 2000/r
    = d/dx 2000*r^(-1)
    = 2000*[-1*r^(-2)*dr/dx]
    = -[2000/(r^2)](dr/dx)
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