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Derivative help

  1. Feb 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Ok, im learning about derivative's, and they seem to elude me for some reason. I have this.

    x2+x

    I know the derivative is 5, and the function is differentiable at 2. But I don't understand how you get it. I know the limit you use to find it, but the shortcut is nxn-1 right? Where does n come from? And x=2 right? Would it be 2*21? But thats not 5, its 4. What am I doing wrong? Please, detailed answers are very very appreciated.


    2. Relevant equations
    Pretty sure that I noted all the nessicary equations above.


    3. The attempt at a solution
    I said what I attempted above.
     
  2. jcsd
  3. Feb 16, 2009 #2
    You've just got to learn the rules of derivatives.

    The derivative is:

    f(x) = 2x + 1

    for the first one, pull out the exponent and make it a coefficient while lowering the exponent by 1 degree. Same thing for the second term.
     
  4. Feb 16, 2009 #3
    The original function x^2+x can be seen as x^2+x^1

    n is the exponent for each x, so for the first x, n=2 and n=1 for the second x

    then use the derivative formula which is dy/dk of f(x) = nx^(n-1)

    which would mean the derivative is 2x^(2-1)+1x^(1-1) which equates to 2x^2+1

    since it asks what the value of dy/dx is at x=2, you plug 2 into the derivative for an answer of 2(2)+1 which equals 5
     
  5. Feb 17, 2009 #4
    Thank you so much.
     
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