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Derivative of the magnitude of a function

  1. Jul 17, 2013 #1
    I just learned that d/dx|r(t)|=1/|r(t) |X r(t)*r'(t), where * is the dot product and X is mutiply. What is the meaning of this statement, especially in relation to d/x r(t)=r'(t)?(Lets say r(t) is the position vector equation.)
     
  2. jcsd
  3. Jul 18, 2013 #2

    mfb

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    ##\frac{r(t)}{|r(t)|}## is just the sign of r(t). If r(t) is positive, it is +1 and you simply get the regular derivative. If r(t) is negative, |r(t)|=-r(t) and this fraction gives the correct minus sign.
     
  4. Jul 19, 2013 #3
    Recall that ## |r(t)| = \sqrt {r(t) \cdot r(t)} ##. Differentiate this.
     
  5. Jul 19, 2013 #4
    A simpler starting point might be to write:

    ## |r(t)|^2 = r(t) \cdot r(t) ##

    Chet
     
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