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% File src/library/stats/man/deriv.Rd
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% File src/library/stats/man/deriv.Rd
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% Part of the R package, https://www.R-project.org
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2013 R Core Team
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% Copyright 1995-2013, 2017 R Core Team
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% Distributed under GPL 2 or later
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% Distributed under GPL 2 or later
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\name{deriv}
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\name{deriv}
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\title{Symbolic and Algorithmic Derivatives of Simple Expressions}
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\title{Symbolic and Algorithmic Derivatives of Simple Expressions}
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\alias{D}
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\alias{D}
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  \code{sinh}, \code{cosh}, \code{sqrt}, \code{pnorm}, \code{dnorm},
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  \code{sinh}, \code{cosh}, \code{sqrt}, \code{pnorm}, \code{dnorm},
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  \code{asin}, \code{acos}, \code{atan}, \code{gamma}, \code{lgamma},
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  \code{asin}, \code{acos}, \code{atan}, \code{gamma}, \code{lgamma},
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  \code{digamma} and \code{trigamma}, as well as \code{psigamma} for one
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  \code{digamma} and \code{trigamma}, as well as \code{psigamma} for one
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  or two arguments (but derivative only with respect to the first).
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  or two arguments (but derivative only with respect to the first).
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  (Note that only the standard normal distribution is considered.)
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  (Note that only the standard normal distribution is considered.)
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  \cr
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  Since \R 3.4.0, the single-variable functions \code{\link{log1p}},
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  \code{expm1}, \code{log2}, \code{log10}, \code{\link{cospi}},
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  \code{sinpi}, \code{tanpi}, \code{\link{factorial}}, and
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  \code{lfactorial} are supported as well.
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}
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}
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\value{
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\value{
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  \code{D} returns a call and therefore can easily be iterated
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  \code{D} returns a call and therefore can easily be iterated
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  for higher derivatives.
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  for higher derivatives.
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## showing the limits of the internal "simplify()" :
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## showing the limits of the internal "simplify()" :
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\dontrun{
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\dontrun{
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-sin(x^2) * (2 * x) * 2 + ((cos(x^2) * (2 * x) * (2 * x) + sin(x^2) *
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-sin(x^2) * (2 * x) * 2 + ((cos(x^2) * (2 * x) * (2 * x) + sin(x^2) *
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    2) * (2 * x) + sin(x^2) * (2 * x) * 2)
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    2) * (2 * x) + sin(x^2) * (2 * x) * 2)
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}
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}
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## New (R 3.4.0, 2017):
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D(quote(log1p(x^2)), "x") ## log1p(x) = log(1 + x)
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stopifnot(identical(
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       D(quote(log1p(x^2)), "x"),
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       D(quote(log(1+x^2)), "x")))
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D(quote(expm1(x^2)), "x") ## expm1(x) = exp(x) - 1
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stopifnot(identical(
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       D(quote(expm1(x^2)), "x") -> Dex1,
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       D(quote(exp(x^2)-1), "x")),
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       identical(Dex1, quote(exp(x^2) * (2 * x))))
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D(quote(sinpi(x^2)), "x") ## sinpi(x) = sin(pi*x)
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D(quote(cospi(x^2)), "x") ## cospi(x) = cos(pi*x)
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D(quote(tanpi(x^2)), "x") ## tanpi(x) = tan(pi*x)
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stopifnot(identical(D(quote(log2 (x^2)), "x"),
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                    quote(2 * x/(x^2 * log(2)))),
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          identical(D(quote(log10(x^2)), "x"),
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                    quote(2 * x/(x^2 * log(10)))))
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}
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}
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\keyword{math}
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\keyword{math}
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\keyword{nonlinear}
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\keyword{nonlinear}