> Again, I don't think these have to be competing notions. In mathematica
> you
> really can work entirely in either paradigm or mix and match.
I totally agree with this.
Here are a couple of different ways in Mathematica
a user can evaluate the derivative of Sin at Pi:
In[5]:=f=Function[{x},Sin[x]]
Out[5]=Function[{x},Sin[x]]
(* Use shorthand ' notation *)
In[7]:=f'[Pi]
Out[7]=-1
(* Using the "Apply" shorthand notation *)
In[9]:=f'@Pi
Out[9]=-1
(* Using built in Sin directly *)
In[26]:=Sin'@Pi
Out[26]=-1
(* Notice Delayed Evaluation is not set *)
In[10]:=g[x_]=D[Sin[x],x]
Out[10]=Cos[x]
In[11]:=g[Pi]
Out[11]=-1
(* Notice here the ":=" delayed evaluation cause this to FAIL *)
In[12]:= h[x_]:=D[Sin[x],x]
In[12]:= h[Pi]
General::ivar: Pi is not a valid variable.
Out[12]= D[0, Pi]
This whole thread is great, lets keep discussing.
-Alex
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