[itex] Show that |x(t)| d/dt |x(t)| = x(t) \cdot x`(t) [/itex]
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