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Logarithmic differentiation

  1. Nov 27, 2009 #1
    find derivative of

    y=(sqrt(8x^4-5))/ (x-1)

    ok...after working out the tricky calculations i get for my final answer:

    (32x^4sqrt(8x^4-5)-64x^3sqrt(8x^4-5)) / (16x^6-32x^5+ 16x^4-10x^2+20x-10)

    I dont know if you want to do the math...im just wondering if i can simplify it anymore. thanks
     
  2. jcsd
  3. Nov 27, 2009 #2

    Mark44

    Staff: Mentor

    I'm pretty sure you didn't do this problem the way you were supposed to. Judging by the title of the thread, you are supposed to do logarithmic differentiation, and I don't see any evidence that you have done this. Instead, it looks like you used the chain rule first and then the quotient rule.

    [tex]y~=~\sqrt{\frac{8x^4 - 5}{x - 1}}[/tex]
    [tex]\Rightarrow ln(y)~=~ln \left(\sqrt{\frac{8x^4 - 5}{x - 1}}\right )[/tex]
    Use the properties of logarithms to write the right side as a difference, and then differentiate with respect to x.
     
  4. Nov 27, 2009 #3
    well what i did was (going from your previous equation):

    ln(y)= ln(sqrt(8x^4-5)) - ln(x-1)...then i just took the derivative and it pretty much eliminated all the ln
     
  5. Nov 27, 2009 #4
    well what i did was (going from your previous equation):

    ln(y)= ln(sqrt(8x^4-5)) - ln(x-1)...then i just took the derivative and it pretty much eliminated all the ln
     
  6. Nov 27, 2009 #5

    Mark44

    Staff: Mentor

    On the left side of the equation you should get 1/y * y'. Did you forget to use the chain rule?
     
  7. Nov 27, 2009 #6
    oh no...i added that... i just forgot to put it up in my above equation
     
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