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Math Help - First and Second partial dervitives

  1. #1
    Member zangestu888's Avatar
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    First and Second partial dervitives

    Am kinda stuck with this function They gave me;

    f(x,t)=ln(x^2(t)-t/x)

    am asked for all first and second order partial dervitves to make the function simpller i did this

    f(x,t)=ln(x^2(t)(1-1/x^3))

    to break up the to ln's

    i get now =ln(x^2t)+ln(1-1/x^3)

    for my second order fxy=0 and for fyx=0 i need someone to confirm these for me is my alebgra correct is what am doing correctby splitting up to logarathimes thank you for ur help!
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  2. #2
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    Hello, zangestu888!

    They gave me: . f(x,t)\:=\:\ln\left(x^2t-\tfrac{t}{x}\right)

    and asked for all first and second order partial dervitves.

    To make the function simpller i did this:
    . . f(x,t)\:=\:\ln\bigg[x^2t\left(1-\frac{1}{x^3}\right)\bigg] to break up the two ln's

    i get now: . \ln(x^2t)+\ln\left(1-\tfrac{1}{x^3}\right)

    For my second order: . f_{xy}= f_{yx}=0 . . . . all this is correct.

    I would break it up like this . . .

    We have: . f(x,t) \;=\;\ln\left(\frac{x^3t - t}{x}\right) \;=\;\ln\left(\frac{t(x^3-1)}{x}\right)

    . . Then: . f(x,t) \;=\;\ln(t) + \ln(x^3-1) - \ln(x)

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