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Derivative using power rule

  1. Jun 18, 2014 #1
    EQJ98dQ.jpg



    can i use the power rule to get the derivative here?

    f ' (x) = 3x^2 - 2(2x^1) + 1
     
  2. jcsd
  3. Jun 18, 2014 #2

    adjacent

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    Of course, why not? Do you use any other rule for that?
    Your answer is correct
     
  4. Jun 18, 2014 #3
    ok good, so i wouldn't go again until there were no powers?

    eg. f ' (x) = 2(3x) - 2(2x) + 1
     
  5. Jun 18, 2014 #4

    adjacent

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    No. Why do you have to differentiate it again? The notation ##f'(x)## means-Differentiate once. Similarly, the notation ##f''(x)## means differentiate twice.

    In leibniz notations ##\frac{\text{d}}{\text{d}x}## means- Differentiate once and ##\frac{\text{d}^2}{\text{d}x^2}## means- differentiate twice and so on.

    In your example,(differentiating twice) you should write ##f''(x)## and this should be equal to the derivative of ##3x^2 - 4x + 1## which is ##6x+4##
    Note that the derivative of a constant (1) is zero.

    So in general, we differentiate the function ##f##, and again differentiate the derivative of the function ##f##, to differentiate ##f## twice. This can also be extended to differentiating 10000 times :wink:
     
    Last edited: Jun 18, 2014
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