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Math Help - Exponential expression

  1. #1
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    Exponential expression

    Can someone give me a hint about transforming  x^{4x} into a quotient? I think it involves setting y equal to it and taking a log or something.
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  2. #2
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    Re: Exponential expression

    can you state the exact problem? What you've written above doesn't make an overwhelming amount of sense.
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  3. #3
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    Re: Exponential expression

    Quote Originally Posted by polarbear73 View Post
    Can someone give me a hint about transforming  x^{4x} into a quotient? I think it involves setting y equal to it and taking a log or something.
    A quotient? What about \dfrac{1}{x^{-4x}}?

    But I suspect you are really talking about the derivative. If we let y= x^{4x} then ln(y)= ln(x^{4x})= 4x ln(x) so that \frac{1}{y} y'= 4 ln(x)+ \frac{4x}{x}= 4 ln(x)+ 4 so that y'= 4y(ln(x)+ 1)= 4x^4(ln(x)+ 1).
    Last edited by HallsofIvy; December 28th 2013 at 04:02 PM.
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  4. #4
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    Re: Exponential expression

    Quote Originally Posted by HallsofIvy View Post
    A quotient? What about \dfrac{1}{x^{-4x}}?

    But I suspect you are really talking about the derivative. If we let y= x^{4x} then ln(y)= ln(x^{4x})= 4x ln(x) so that \frac{1}{y} y'= 4 ln(x)+ \frac{4x}{x}= 4 ln(x)+ 4 so that y'= 4y(ln(x)+ 1)= 4x^4(ln(x)+ 1).
    That last equality should be y' = 4x^{4x}\left(\ln(x) + 1\right)
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  5. #5
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    Re: Exponential expression

    Yes, thanks.
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