# Deriv

## Symbolic differentiation

The original version of this software was written in R by Andrew Clausen (clausen at econ.upenn.edu) in 2007.

Mark Reid (mark.reid at anu.edu.au) sent a patch, applied 21/2/2009.

In 2014, Andrew has passed the maintenance to Serguei Sokol (sokol at insa-toulouse.fr). Since then, the software was deeply rewritten and completed.

Main new features include:

- new derivative engine allowing simple syntaxe for differentiation rules;
- many new functions are added to the rule table;
- custom differentiation rules can be added by user;
- automatic differentiation (AD) of a code with multiple assignement operators;
- when taking derivative of a function Deriv() returns a function too. The later can be called with the same arguments as the original function;
- can differentiate by variables stored in vectors or lists, e.g.
`param$theta`

or`x[1]`

,`x[2]`

etc. - simplifications are extended to rational expressions and factorizations;
- expression caching is enabled by default;
- Deriv() is made the only entry point for all types of entries:
- expression
- language
- function
- right hand side of a formula
- character string
- plain unevaluated code

- few unit tests were added to the package

## Installation

`> devtools::install_github("sgsokol/Deriv")`

## Usage

In R session do:

```
> library(Deriv)
> f <- function(x, n=2) x^n+sin(n*x) # user defined function to diffierentiate
> (df <- Deriv(f)) # -> c(x = n * x^(n - 1) + n * cos(n * x), n = log(x) * x^n + x * cos(n * x))
> df(2, 3) # -> x n
# -> 14.880511 7.465518
> Deriv(expression(f(y, 3)), "y") # -> expression(3 * y^2 + 3 * cos(3 * y))
> Deriv(~ f(y, 3), "y") # -> 3 * y^2 + 3 * cos(3 * y)
> y <- 2; eval(Deriv(~ f(y, 3), "y")) # -> 14.88051
```

For more information and examples:

`> ?Deriv`