Evaluate list of functions at a certain point

I have a list of functions (actually they are derivatives) of the type:

{D[g[x,y],x],D[g[x,y],y]}

I would like to evaluate all of these functions at a point, say,[0,0], creating a list of the type:

{D[g[x,y],x][0,0],D[g[x,y],y][0,0]}

Is this possible?
Thanks.

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are you sure you want D[g[x,y],x][0,0]?
– Kuba
Jan 29 ’15 at 17:16

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2 Answers
2

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To get what you asked for, you can use

dl = {D[g[x, y], x], D[g[x, y], y]};
Through @ dl[0, 0]

However, as noted by @Kuba, you probably want something like

ClearAll[foo];
foo = Through@(Function[{x, y}, #] & /@ dl)@## &;
foo[0, 0]

  

 

Thats exactly it. Thanks.
– user191919
Jan 29 ’15 at 17:17

  

 

@user191919, my pleasure..
– kglr
Jan 29 ’15 at 17:20

f[x_] := x^2;
g[x_] := x^3;

{f[#], g[#]} & @ 5

(*
{25, 125}
*)

Or for your example:

f[x_, y_] := x^2 + y;
g[x_, y_] := Sin[x] + y^3;

{D[f[x, y], x], D[g[x, y], y]} /. {x -> 3, y -> 4}

(*
{6, 48}
*)