How to create lagged differences by group in R?

I have the following dataframe:

df <- data.frame(id = c("1", "1", "1", "2", "2"), 
                 x = c(12, 20, 24, 10, 14))

id   x
 1  12
 1  20
 1  24
 2  10
 2  14

I’d like to obain the lagged differences of x per id. The expected result:

id   x
 1  12
 1   8
 1   4
 2  10
 2   4

A dplyr solution is preferable.

Note that this question is not a duplicate, since the group refers to an ID in my case, not an unordered category.

>Solution :

Using diff

library(dplyr)

df %>% 
  mutate(x = c(x[1], diff(x)), .by = id)
  id  x
1  1 12
2  1  8
3  1  4
4  2 10
5  2  4