Pass a symbolic function as input to a function without passing its inputs

Hello,

I have a question and I believe the best is to go to an example from the begining. Consider the following

syms x y
syms mu(x,y)
syms par [1 3]
mu(x,y)=par(1)*x^2*y+par(2)*x*y+par(3);
test(mu,par)

where test.m is defined as bellow

function test(f,par)
gradient(f,par);   %Works
diff(f,x) ;   %does not work 
end

If I try g = test(mu,par) it works well. However, I cannot calculate stuff like diff(f,x) simply because inside the 'test.m' function it is not defined. Of course, I could pass x,y as nputs of test.m as bellow

function test(f,par,x,y)
gradient(f,par);   %Works
diff(f,x)   %Works
end

My question: Is there a way not to pass parameters (like vector par above) and state variables (like x and y above) and only pass the function mu? Of course, inside the test.m x and y are not recognized. However, there is a nice mtlab command 'argnames' which let us know the inputs of a function. So, I am wondering whether I can only pass the function 'mu' to test.m and then inside test.m use the command 'argnames' to fins the inputs of 'mu'. Is this possible? I mean to say that I wish to have a test.m to be defined as bellow

function test(f,par)
USE ARGNAMES COMMAND TO INVIKE THE INPUTS OF f. THEN DO THE FOLLOWING
diff(f,x)  
end

Answer 1

[Matt J]

You seem to have answered your own question...

function [g,d]=Test(f,par)

    g=gradient(f,par);  
    
     args=argnames(f);
    d=diff(f,args(1)) ;   
    
end