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Piecewise Functions


I am trying to use Mma to solve a model where the system behaves a 
certain way up to a point, and an entirely different way after that 
point.  The result is something like:

f[x_/;x<4]:=0
f[x_/;x>=4]:=InterpolatingFunction<<...>>

This part I can get to work no problem.  For part of my analysis, I would 
like to take the derivative of the function, but all I get is an identity

In[5]
	f'[x]

Out[5]
	f'[x]

Can anyone help?

+----------------------------+   
|                            |   I understand mine's a risky plan,
|   Greg Anderson            |   and your system can't miss
|   dwarf at wam.umd.edu        |   but is security, after all a cause
|   timbwolf at eng.umd.edu     |   or symptom of happiness.
|                            |   
+----------------------------+   Dream Theater -- A Matter of Time

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