Derivative of the magnitude of a function

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  • #1
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Main Question or Discussion Point

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.)
 

Answers and Replies

  • #2
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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.
 
  • #3
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Recall that ## |r(t)| = \sqrt {r(t) \cdot r(t)} ##. Differentiate this.
 
  • #4
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Recall that ## |r(t)| = \sqrt {r(t) \cdot r(t)} ##. Differentiate this.
A simpler starting point might be to write:

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

Chet
 

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