# [R] Derivative of a function

Martin Maechler maechler at stat.math.ethz.ch
Tue Jul 5 15:37:14 CEST 2005

```>>>>> "Gabor" == Gabor Grothendieck <ggrothendieck at gmail.com>
>>>>>     on Tue, 5 Jul 2005 09:14:20 -0400 writes:

Gabor> On 7/4/05, Gabriel Rodrigues Alves Margarido
Gabor> <gramarga at carpa.ciagri.usp.br> wrote:
>> 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.
>>

Gabor> Note sure if this is good enough but in the following you can
Gabor> replace 1,2 in the third line with other indices to extract out any
Gabor> matrix component and differentiate it.  e is a list that contains the
Gabor> 4 expressions and idx[i,j] gives the index in e that contains
Gabor> the i,j-th expression:

Gabor> e <- lapply(1:4, function(i) bquote(x^.(i)))
Gabor> idx <- matrix(1:4, 2)
Gabor> e12 <- e[idx[1,2]][[1]]
Gabor> D(e12, "x")

neat, Gabor!

The following may also be useful {after the initial "e <- lapply(....)"}:

De <- lapply(e, D, "x")
dim(De) <- c(2,2)

> De[[1,2]]
3 * x^2
> De[[2,2]]
4 * x^3

--
Martin Maechler, ETH Zurich

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