Suppose I have a simple function that returns a matrix, such as:

test <- function(x){ return(matrix(c(x,x^2,x^3,x^4),2,2)) }

so that test returns:
[ x    x^3 ]
[ x^2   x^4 ]

Is it possible for me to get the derivative of an expression such as:

c(1,0) %*% test() %*% c(0,1)

The vectors are used just to "index" the matrix.
I don't want a value, but the expression to work with (in that case,
the expected expression would be 3*x^2)...

Tried functions D and deriv in many ways, but no success.
I will be grateful if anyone can help.

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