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Finding various derivatives - Help!

  1. Sep 15, 2005 #1
    find

    1 .derivaive of y, y = x^a^x

    2. nth derivaive of (x+p)^-1 p is constant

    3. nth derivaive of (ax+b)/(cx+d)

    4. nth derivaive of y = sin (^2) x
     
  2. jcsd
  3. Sep 15, 2005 #2

    HallsofIvy

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    Looks like homework to me. Is it?

    The first one like you need to work with ln(y)= (a^x)ln x.

    The others, just calculate two or three derivatives and see if you can spot a pattern.
     
  4. Sep 16, 2005 #3
    i know how to do qs 1
     
  5. Sep 16, 2005 #4

    HallsofIvy

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    Did you read what I wrote before?

    For [tex]y= x^{(a^x)}[/tex], take the logarithm of both sides:

    ln(y)= axln(x). Now differentiate both sides, with respect to x.
    (You will need to use the chain rule on the left side and the product rule on the right.)
     
  6. Sep 16, 2005 #5
    i mean i know how to do the first one now
     
  7. Sep 17, 2005 #6

    VietDao29

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    For #2, you can use: (ab)' = b ab - 1.
    Then note that (x + p)' = 1.
    For example: [tex]y' = \left( \frac{1}{x + p} \right)' = -\frac{1}{(x + p) ^ 2}[/tex]
    [tex]y'' = (y')' = -\left( \frac{1}{(x + p) ^ 2} \right)' = 2\frac{1}{(x + p) ^ 3}[/tex]
    So [tex]y ^ {(n)} \ = \ ?[/tex]
    -----------------------
    For #3, you need to arrange [tex]\frac{ax + b}{cx + d}[/tex] into something like: [tex]C + \frac{A}{cx + d}[/tex], where C, and A = const.
    Then you just do the same like #2.
    -----------------------
    For #4, you can try to take 1st, 2nd, 3rd, 4th, ... derivative of the function and see the rule.
    Note that 2sin(x)cos(x) = sin(2x).
    Viet Dao,
     
  8. Sep 17, 2005 #7
    1. ln y = a^x lnx
    y'/y = [xa^(x-1)]lnx + [(1/x)a^x]
    y' = y[[xa^(x-1)]lnx + [(1/x)a^x]]

    2. -1(x+p)^-2
    too lazyt to do the rest..
     
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