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Thread: Partial Derivatives

  1. #1
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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 $\displaystyle \partial$ and treat all other independent variables as constants until we are done.

    For example,

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

    Hope this helps.
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