# Derivative of a special function

1. Aug 25, 2010

### orienst

Let f(x) be the following function:

f(x)=$$\infty$$,if x<0 or x>a;f(x)=0,if 0<x<a.

What’s the derivative of f(x) at x=0 and x=a? I know that the derivative of step function is $$\delta$$(x) , but what will occur if the jump is infinite?

2. Aug 25, 2010

### JJacquelin

f ' (x) = dx*f(x)

3. Aug 25, 2010

### mathman

In general the derivative of a jump of size a at u is aδ(x-u). your a is -∞ and u=0.

4. Aug 29, 2010