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Math Help - Partial Derivatives

  1. #1
    Newbie
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    Mar 2009
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    Partial Derivatives

    I was having problems with the question:

    Find all first and second partial derivatives of f(x, t) = ln (x^2*t − t /x)?


    
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  2. #2
    Senior Member
    Joined
    Dec 2008
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    Finding a partial derivative is just like finding an ordinary derivative. We differentiate with respect to the variable of the lower \partial and treat all other independent variables as constants until we are done.

    For example,

    \begin{aligned}<br />
\frac{\partial f}{\partial x} &= \frac{\partial}{\partial x}\ln\left(x^2t-\frac{t}{x}\right)\\<br />
&= \frac{1}{x^2t-\frac{t}{x}}\cdot\left(2xt+\frac{t}{x^2}\right)\;\  ;\;\;\;\;\;\;\;\;x^2t-\frac{t}{x}>0.<br />
\end{aligned}<br />

    Hope this helps.
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