# Is mod x differentiable at all points

1. Oct 4, 2011

### sphyics

f(x)= mod x is this function differentiable at all points other than 0.

2. Oct 4, 2011

### CompuChip

What do you mean by f(x) = mod x?
Usually, mod is used in an expression like "6 mod 4 = 2", and "mod 4" by itself doesn't really mean anything.

Did you mean "f(x) = |x|", the absolute value of x?
In that case, the answer is yes: you can easily see this by showing that it is equivalent to x for x > 0 and -x for x < 0. To prove that it is non-differentiable at x = 0, you need to do a little work, but that's still straightforward.

3. Oct 4, 2011

### sphyics

yes its absolute value of x :)

4. Oct 4, 2011

### 1mmorta1

Why did you use the term mod for absolute value? I'm not familiar with that application of mod.

5. Oct 4, 2011

### gb7nash

I think the OP meant modulus, which is another term for absolute value.

6. Oct 4, 2011

### 1mmorta1

Don't use unapproved abreviations! Haha, i got confused.

7. Oct 5, 2011

### Bacle

Yes; one way of seeing it is look at |x| as the piecewise function:

f(x)=x , if x≥0
f(x)=-x, if x≤0

Then the function is linear , and if you accept that for n>1, d/dx(xn)=nxn-1, then f is differentiable in (0,∞), and in (-∞,0), and the only possible problem is at x=0.