> deriv(expression(log(sigma) - log(sigma^2 + (x - mu)^2)), "mu")
expression({
    .expr3 <- x - mu
    .expr5 <- sigma^2 + .expr3^2
    .value <- log(sigma) - log(.expr5)
    .grad <- array(0, c(length(.value), 1), list(NULL, c("mu")))
    .grad[, "mu"] <- 2 * .expr3/.expr5
    attr(.value, "gradient") <- .grad
    .value
})
> deriv(expression(sin(x)), "x")
expression({
    .value <- sin(x)
    .grad <- array(0, c(length(.value), 1), list(NULL, c("x")))
    .grad[, "x"] <- cos(x)
    attr(.value, "gradient") <- .grad
    .value
})

#### stupid !!!!!
> deriv(expression(lgamma(x)), "x")
Error in deriv.default(expression(lgamma(x)), "x") :
        Function `lgamma' is not in the derivatives table

#### for those that know calculus, the derivative is the digamma function
> epsilon <- 1e-9
> (lgamma(2 + epsilon) - lgamma(2)) / epsilon
[1] 0.4227843
> digamma(2)
[1] 0.4227843

> fred <- function(y) function(x) x + y
> sally <- fred(10)
> sally
function(x) x + y
<environment: 0x8eeb7b8>
> sally(2:4)
[1] 12 13 14

#### comments added after class
> environment(fun = sally)
<environment: 0x8eeb7b8>
> get("y", environment(fun = sally))
[1] 10
> y
Error: Object "y" not found