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Hard Derivative

  1. Feb 6, 2013 #1
    1. The problem statement, all variables and given/known data

    ([3√(x^2+4)^4]^2

    2. Relevant equations

    None needed.
    Chain rule
    product rule etc

    3. The attempt at a solution
    I stopped at:

    [((x^2+4)^4)^1/3]^2

    So I have 3 exponents. I don't know how to simplify this in order to move on to do the chain rule or whatever rule that comes next. The exponents are killing me
     
  2. jcsd
  3. Feb 6, 2013 #2

    Mark44

    Staff: Mentor

    Although you can't tell from the above, from your work below, it appears that the radical is a cube root.

    Is this what you're trying to differentiate?
    ## (\sqrt[3]{(x^2 + 4)^4})^2##
    What does (ar)s simplify to?
     
  4. Feb 6, 2013 #3
    I think it simplified down to (x^2+4)^8/3
    I multiplied the exponents: 1/3 * 4/1 * 2/1 = 8/3
     
  5. Feb 6, 2013 #4

    Mark44

    Staff: Mentor

    OK, that's the first step.

    Now, what is d/dx[(x2 + 4)8/3]?
     
  6. Feb 7, 2013 #5
    I figured it out. Thank you. My main issue was with the exponents in regards to if I had to multiply all of them together which was true.
     
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