# Derivative of this piecewise function?

1. Oct 2, 2011

### Inertigratus

1. The problem statement, all variables and given/known data
I have this piecewise defined function and am wondering if the derivative is supposed to be piecewise defined as well?
Or could I just write it out on a line like a "normal" function?

2. Relevant equations
x(t) = {-14t : 0$\leq$|t|< 1, 2sgn(t) : 1$\leq$|t|< 7, (-12/7)sgn(t) : 7$\leq$|t|< 14, 0 : 14$\leq$|t| }

3. The attempt at a solution
I'm thinking I can write the derivative as a normal function. Since the piecewise functions are defined with no time-jumps between them and the derivative will have Dirac delta functions defined at the function incontinuities. Therefor the derivative should be continuous on the interval:
0$\leq$|t|$\leq$14.
Is this correct?

2. Oct 2, 2011

### SammyS

Staff Emeritus
Graph the function.

That should tell you the answer.

There are no gaps in the function definition -- if you are referring to the fact that the domain of the function is (-∞, ∞). However, this function has discontinuities at several places. Its derivative has even more discontinuities than the function itself !

3. Oct 2, 2011

### Inertigratus

Oh right, I asked a little too quick before thinking it through enough.
Thanks!