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Math Help - Derivative of a (very) simple log function

  1. #1
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    Derivative of a (very) simple log function

    y = (ln x)^4

    The given answer is 4/x (ln x)^3. The problem I'm having is, isn't it one of the rules that an exponent is transferred to the base? I mean, should (ln x)^4 become 4 (ln x)? The answer used the chain rule right away without modifying the function.
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  2. #2
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    Quote Originally Posted by Archduke01 View Post
    y = (ln x)^4

    I mean, should (ln x)^4 become 4 (ln x)?
    No.  ln(x^4) = 4\ln(x)

    This is different from  (\ln(x))^4 . For ln(x^4) the power only applies to 'x' whilst your question concerns the whole term ln(x) raised to the 4th power.
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