# Homework Help: Show that |x(t)|d/dt*|x(t)| = x(t) . x(t)

1. Apr 16, 2013

### Smazmbazm

1. The problem statement, all variables and given/known data

$Show that |x(t)| d/dt |x(t)| = x(t) \cdot x(t)$

3. The attempt at a solution

I don't know what they want to see here but my go at this is to take x(t) = 2t. Differentiating this gives x(t) = 2.

Taking the normal of both |x(t)| and |x(t)| gives 2t and 2, respectively.

So 2t * 2 = 4t.

Then just do the same with x(t) and x`(t) to get 4t again?

I don't know if this will suffice as a proper answer

2. Apr 16, 2013

### Bacle2

I assume they expect you to show the result for any path x(t), not just x(t)=2t .

I think working with the cases (for the absolute value) ; when is x(t)>0 , when is it <0 ,=0 ,

Hint: Use the fact that $\frac{d}{dt} |t|=\frac{t}{|t|}$ with the chain rule to compute your derivative in the two cases $x(t) > 0$ and $x(t) < 0$ . You have to consider the case $x(t)=0$ carefully.