Extract the k-th derivative from a nested dual result

After evaluating a function on a dual created by dual_variable_n, use deriv_n to extract any derivative from 0 (the function value) up to the seeded order.

deriv_n(d, k)

Arguments

d

A (possibly nested) dual number, or a numeric.

k

A non-negative integer: 0 for the function value, 1 for the first derivative, etc.

Value

A numeric value.

Examples

x <- dual_variable_n(1, order = 3)
r <- exp(x)
deriv_n(r, 0)  # exp(1) = 2.718...
#> [1] 2.718282
deriv_n(r, 1)  # exp(1)
#> [1] 2.718282
deriv_n(r, 2)  # exp(1)
#> [1] 2.718282
deriv_n(r, 3)  # exp(1)
#> [1] 2.718282