# Derivative of the magnitude of a function

## 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.)

mfb
Mentor
##\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.

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

Chestermiller
Mentor
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