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I have sets of functions of material parameters where the first input argument denotes the material. Here's a simple version:

tf1["a", x_] = x^3;
tf1["b", x_] = x^4;

Now, I'd like to make a function which needs the derivative of tf1 with respect to x. My goal is the following:

myderivative["a",x]=3 x^2

myderivative["b",x]=4 x^3

The way to implement this should be something like

myderivative[i_, x_] = Derivative[2][tf1[i, #] &][x]
myderivativeb[i_, x_] = Derivative[0, 2][tf1][i, x]

I even tried

tf2[i_] = tf1[i, #] &
myderivative2[i_, x_] = Derivative[2][tf2[i]][x]

But all of the variants return

(tf1^(0,2))[i,x]

I tried using SetDelayed (:=) in all of the above variants but this doesn't return anything else. Also, approaches with D or [Esc] pd [Esc] failed.

So how do I take the derivative of this overloaded function? It should also work with distinct numbers, e.g. I expect

myderivative["a",2]=12

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  • $\begingroup$ der[i_, x_] := D[tf1[i, x], x] worked for me? $\endgroup$
    – Pillsy
    Apr 6, 2017 at 16:35
  • $\begingroup$ If tf1 has a first variable, you should define it as: tf1[myname_?String, x_] and define the specific functions for myname = "a" and "b". $\endgroup$ Apr 6, 2017 at 16:36
  • $\begingroup$ @Pillsy perfect, this seems like the only combination I didn't try... (I was mostly trying pure functions as the argument). Thanks! $\endgroup$ Apr 6, 2017 at 16:39
  • $\begingroup$ @DavidG.Stork this is unrelated to the derivative, but a short example would help me a lot. And maybe a hint why this is better than my way. Thank you very much! $\endgroup$ Apr 6, 2017 at 16:40
  • $\begingroup$ @Pillsy however, your solution doesn't work for der["a",3], for example. There's an error "General::ivar" $\endgroup$ Apr 6, 2017 at 16:50

2 Answers 2

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I suggest doing the derivative and then substituting in a value. This can be done as follows:

der[i_, x_] :=
  D[tf1[i, \[FormalX]], \[FormalX]] /. \[FormalX] -> x;

Using a "formal" variable means you don't have to worry about it being defined in scope and screwing things up.

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  • $\begingroup$ great! I tried substituting and ReplaceAll but not with the formal variable. Thank you so much! $\endgroup$ Apr 7, 2017 at 8:05
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tf1[myname_String, x_] := Which[myname == "a", x^3, myname == "b", x^4];

D[tf1["a", x], x]

(* 3 x^2 *)

D[tf1["b", x], x]

(* 4 x^3 *)

If you have a "default" function for all string variables not yet entered, then:

tf1[myname_String, x_] := 
  Which[myname == "a", x^3, myname == "b", x^4, True, Sin[x]];

D[ft1["c",x],x]

(* Cos[x] *)

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  • $\begingroup$ since I have many string parameters "a", "b", "c", etc I wanted to save the time of explicitely deriving all of them but wanted to do it as stated in the question (variable i). This is not possible, again giving the error "General::ivar" when putting in values $\endgroup$ Apr 6, 2017 at 16:55
  • $\begingroup$ What is a "question variable"? $\endgroup$ Apr 6, 2017 at 23:51
  • $\begingroup$ you didn't see the paranthese. Basically, Pillsy's answer is what I was looking for, as it keeps the variable i in the derivative. $\endgroup$ Apr 7, 2017 at 8:08

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