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Is the derivative of 2x^2 = 4x or 8x?

  1. Jan 5, 2016 #1
    Call me crazy, but I do recall the power rule of integration viz: f(x) = x^n, f(x)' = n*x^n-1. Therefore, it seems as though 2x^2 would have a derivative of 4x. Fine. So why have I encountered someone else claiming that it's 8x? WHAT?! Who's right?
     
  2. jcsd
  3. Jan 5, 2016 #2

    Mark44

    Staff: Mentor

    Do you really mean ##n * x^n - 1##? That's what you wrote. As inline text, use parentheses -- n*x^(n - 1)

    Yes. ##d/dx(2x^2) = 4x##.
    Maybe they're working a different problem.
     
  4. Jan 5, 2016 #3

    Krylov

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    I can think of many reasons, but none of them involve mathematics.
     
  5. Jan 5, 2016 #4
    I haven't yet applied Latex (I'm going to read the article after I finish reading this other long article on u-substitution - I'm really trying here), but what I mean is the super basic power rule of derivatives: f(x) = xn, f(x)' = nxn-1
     
  6. Jan 5, 2016 #5

    Krylov

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    You are right, the other person must have a brain worm. Also, I would write ##f'(x)## instead of ##f(x)'##.

    EDIT: Could you prove that the other has a brain worm?
     
    Last edited: Jan 5, 2016
  7. Jan 5, 2016 #6
    And just for the record: I meant DERIVATION, not integration.o0)
     
  8. Jan 6, 2016 #7

    Mark44

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    Contrary to much popular opinion, the opposite of integration is differentiation, not derivation. You can derive the quadratic formula using the completion of squares technique, but you differentiate ##2x^2## to get the derivative, 4x. Yes, English is weird...
     
  9. Jan 6, 2016 #8

    fresh_42

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    Thanks for clarifying. I sometimes get confused because the result of differentiation is a derivative (obeying the product rule) and the result of integration is an anti-derivative. Is that correct or am I still confusing terms?
     
  10. Jan 6, 2016 #9

    Mark44

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    No, you have it right.
     
  11. Jan 6, 2016 #10

    Erland

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    Perhaps "someone else" meant (2x)2, which has the derivative 8x.
     
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