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Differentiation math homework

  1. May 12, 2007 #1

    Air

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    Differentiate with respect to x

    dy = 3x^2 - 5√x + 1/2x^2
    dx

    __________________________________________

    I don't understand how to differentiate this part: 5√x + 1/2x^2. I think changing it to indices form would be: x^1/5 + (2x)^-2?

    How can it be worked out? :confused:
     
  2. jcsd
  3. May 12, 2007 #2
    [tex]5\sqrt{x}[/tex] is not [tex](x)^{\frac{1}{5}}[/tex]. It is five times [tex](x)^{\frac{1}{2}}[/tex].

    The last term is a bit ambiguous, the way you've typed it. Is it [tex]\frac{1}{2}x^2[/tex] or [tex]\frac{1}{2x^2}[/tex]? Anyway, neither cannot be simplified to (2x)^-2.
     
  4. May 12, 2007 #3

    Air

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    That makes more sense. :biggrin:

    It's [tex]\frac{1}{2x^2}[/tex]
     
  5. May 12, 2007 #4
    It's then (1/2)(x^-2). (2x)^-2 would be (1/4)(x^-2).
     
  6. May 12, 2007 #5

    Air

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    Ok. I understand. Thanks for the help. :biggrin:
     
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