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Some differentiations

  1. Jan 23, 2014 #1
    I have some important questions and essentials for understand some theories. They are six:
    given f(r(t)), f(r(u, v)), f(r(u(t), v(t))), f(r(t)), f(r(u, v)) and f(r(u(t), v(t))). How compute its derivatives wrt independent variables?

    Unfortunately, I just know the answer for 1nd:
    [tex]\frac{df}{dt}=\frac{df}{d\vec{r}}\cdot \frac{d\vec{r}}{dt}[/tex]
    I don't know equate the other derivatives.
  2. jcsd
  3. Jan 24, 2014 #2

    Simon Bridge

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    Where you have more than one variable, you use partial derivatives.
    When the variables are nested, just repeat the chain rule.
    Recall how to differentiate a vector.
  4. Jan 24, 2014 #3
    But I think that chain rule will expand to much. I think if exist another way more compact for these differentations... some so so like
    ##\frac{d^2f}{du dv}=\frac{d^2 f}{d\vec{r}^T d\vec{r}}\cdot \frac{d\vec{r}}{du}\times \frac{d\vec{r}}{dv}##
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