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Simple differentiation for YOU PPL!

  1. Nov 2, 2005 #1
    how do I differentiate 4*x^(2x)?
    The professor explained to the class while i was sleeping...
    and I dont quite get what my fd was talking about...

    can anyone help?
    I know x^(2x) is different from a constant to (2x)
    but I dont no how to do it...

    is the answer (x^x)(lnx)+(x^x)
    if so could you guys explain it step by step? THANX!!!!!
     
  2. jcsd
  3. Nov 2, 2005 #2
    Call it a function, y:
    y = 4x^(2x)
    There's one easy way to do it that I can think of...
    First thing we do, let's ignore the 4.... it'll probably end up confusing you; what we'll do with the final answer is multiply it before, so let's define a new function z:
    z = x^(2x)
    Apply log to both sides...
    log z = 2x log x
    Use the chain and product rule..
    z'/z = 2log x + 2
    z' = (x^2x)(2log x + 2)
    Now, times the whole thing by 4...
    y' = (4x^2x)(2log x + 2)

    By the way I think this should be in the homework help forum or the calculus forum..
     
  4. Nov 9, 2005 #3
    Thank You!!!!!

    You Are My Savior!!!!

    Thanks Alot!!!!!

    I Love You!
     
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