Derivative of the magnitude of a function

[better361]

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.)

 

[mfb]

$\frac{r(t)}{|r(t)|}$ 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.

 

[voko]

Recall that $|r(t)| = \sqrt {r(t) \cdot r(t)}$. Differentiate this.

 

[Chestermiller]

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