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Devivativing problems

  1. Nov 3, 2004 #1
    Hi. I can't get what I'm doing wrong here. If somebody points that out, I'm really gratefull.

    [tex]u = (6 + 2x^2)^3[/tex]
    [tex]d(u) = 3(6+2x^2)^2 d(6+2x^2)=3(6+2x^2)^2 d(6) + d(2x^2)
    = [3(6+2x^2)^2 * 0 + 4x]dx = 4xdx[/tex]
    Then I want to draw a tangent on the point, which acctually lies on the line(!), (1, 512) to check the derivative.
    [tex]l(x)=f'(a)(x-a)+b=4(x-1)+512=4x+508[/tex] Which don't intersect the curve at (1, 512)...

    Please correct every misstake I've made. Yes, they could be many; I'm not so good on this stuff. :biggrin:
  2. jcsd
  3. Nov 3, 2004 #2

    matt grime

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    You've forgotten that there is a bracket around 6+2x^3 in the second line of the maths.

    You've misspelled mistake too. And who said irony is dead?

    Anyway, du/dx is not 4x as should be obvious to you (u if you multiplied it out would have an x^6 term in it and hence du/dx must have an x^5 term in it.
  4. Nov 3, 2004 #3
    Hmm. I'm sorry, but I don't get it. Can you please be a little more specific. This stuff is doing me crazy!
  5. Nov 3, 2004 #4

    matt grime

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    Go through the second line of maths look how you write, in effect:

    A(B+C) = AB + C.

    when you go "across" the second equals sign in the line, ie from

    [tex](6+2x^2)^2 d(6+2x^2)=3(6+2x^2)^2 d(6) + d(2x^2)[/tex]

    they aren't equal. Your algebraic manipulation is wrong.
  6. Nov 3, 2004 #5
    Ahh! Thanks! That should I've noticed...
    [tex]d(y)=3[(x^2+5)^2][d(x^2+5)]=3[(x^2+5)^2][d(x^2)+d(5)] = 3[(x^2+5)^2]2x=6x(x^2+5)^2[/tex]
    Last edited: Nov 3, 2004
  7. Nov 3, 2004 #6


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    Should be
    [tex]d(u)= 3(6+2x^2)^2 d(6+2x^2)= 3(6+2x^2)^2[d(6)+ d(2x^2)][/tex]
    [tex]d(u)= 3(6+2x^2)^2[0+ 4xdx]= 12x(6+2x^2)^2dx[/tex].

    What you give: l(x)= 4x+ 508 certainly does intersect the curve at (1, 512): l(1)= 4+ 508= 512. It just isn't tangent to the curve because your f'(1) is incorrect.

    When x= 1, du/dx= 12(1)(8)2= 768.
    The tangent line should be y= 768(x-1)+ 512= 768x- 256.

    That works nicely. (Aren't graphing calculators wonderful!)
  8. Nov 4, 2004 #7
    Mine doesn't give me that though. :grumpy:
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