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Math Help - Where does the square come from?

  1. #1
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    Where does the square come from?

    I need to find the derivative of the following..

    g(t) = ln(t2e-t^2)

    g(t) = ln t^2 + ln e^(-t^2)
    = g(t) = 2 ln t  +  -t^2 (ln e = 1, right?)

    g '(t)=  2 ( 1 / t ) + (-2t)
    g '(t)= 2 - 2t / t

    g '(t) = 2(1 - t) / t

    According to my textbook though, I should have gotten this...

    g '(t) = 2(1-t^2) / t

    Where is the t2 coming from?
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  2. #2
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    Re: Where does the square come from?

    Quote Originally Posted by astuart View Post
    I need to find the derivative of the following..

    g(t) = ln(t2e-t^2)

    g(t) = ln t^2 + ln e^(-t^2)
    = g(t) = 2 ln t  +  -t^2 (ln e = 1, right?)

    g '(t)=  2 ( 1 / t ) + (-2t)
    g '(t)= 2 - 2t / t

    g '(t) = 2(1 - t) / t

    According to my textbook though, I should have gotten this...

    g '(t) = 2(1-t^2) / t

    Where is the t2 coming from?
    \displaystyle \begin{align*} \frac{2}{t} - 2t &= \frac{2}{t} - \frac{2t^2}{t} \\ &= \frac{2 - 2t^2}{t} \end{align*}
    Thanks from astuart
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  3. #3
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    Re: Where does the square come from?

    Quote Originally Posted by Prove It View Post
    \displaystyle \begin{align*} \frac{2}{t} - 2t &= \frac{2}{t} - \frac{2t^2}{t} \\ &= \frac{2 - 2t^2}{t} \end{align*}
    Ah. Is it from this??

    2t / t - 2t / 1 (t)  =  2t / t  -  2t^2 - t

    Basically, to subtract fractions they must have the same denominator - therefore to get 2t to be 2t / t, it has to be multiplied by t?
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