Derivative of a special function

[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?

 

[JJacquelin]

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

 

[mathman]

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

 

[orienst]

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

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

Thanks for your reply.

 

[HallsofIvy]

Note that the "function" you give is not really a function. And Jjaquelin and mathman had to use "generalized functions" to give an answer.