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Homework Help: Help wid differn when to take logs of both sides

  1. Apr 23, 2010 #1
    1. The problem statement, all variables and given/known data

    solve via newt raphson iterative method to 4dp

    Find the solution x= 1/(1+x^x) to 4dp beginning at x=1


    2. Relevant equations


    Now the formula for this is

    x1= x0 – f(x0)/f’(x0)

    Now what I did was rearrange so f(x)= x( 1+x^x)-1=0

    I need to differentiatie this expression

    So say I called it y= x( 1+x^x)-1

    Could I proceed by taking logs of both sides


    i.e (an example where I saw people take logs of boths ides was when y=x^x and therefore lny=x^x) is that only for when there is one term equal to another




    3. The attempt at a solution

    how I attempted it was as follows

    y= x + x^(x+1) -1

    lny = lnx +(x+1)lnx - ln1

    lny= lnx +xlnx +lnx –ln1

    1/y dy/dx= 1/x + lnx +1

    dy/dx = (x + x^(x+1) -1) (1/x + lnx +1)

    now this feels wrong to me 
     
  2. jcsd
  3. Apr 23, 2010 #2
    y=x(1+x^x)-1=f(x)=0 => ln(y)=ln(0) ?

    why not differentiate f(x)=x(1+x^x)-1 and use the log method to differentiate just x^x part?
     
  4. Apr 23, 2010 #3

    the f(x) simpliefies to x + x^(x+1) -1

    do you mean differentiate the x^(x+1) seperately

    i don't think it can work like that?

    do i not need something to equal something before i can apply teh log thing
     
  5. Apr 23, 2010 #4
    yes, to differentiate the x^(x+1)
    f(x)=x+x^(x+1)-1

    let y=x^(x+1)
    apply the log trick to y to get y' and you will get f'(x) as
    f'(x)=1+y'
     
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