diff --git a/DESCRIPTION b/DESCRIPTION
index f0e5690..12e7a0f 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,7 +1,7 @@
 Package: mpoly
 Type: Package
 Title: Symbolic Computation and More with Multivariate Polynomials
-Version: 1.1.1.901
+Version: 1.1.1.902
 URL: https://github.com/dkahle/mpoly
 BugReports: https://github.com/dkahle/mpoly/issues
 Authors@R: person("David", "Kahle", email = "david@kahle.io", role = c("aut", "cre"), comment = c(ORCID = "0000-0002-9999-1558"))
diff --git a/NAMESPACE b/NAMESPACE
index 9ee275a..a6b6b06 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -69,6 +69,7 @@ export(mp)
 export(mpoly)
 export(mpolyList)
 export(multideg)
+export(normalize_coefficients)
 export(partitions)
 export(permutations)
 export(plug)
diff --git a/NEWS.md b/NEWS.md
index 4d6e6c4..222cb8b 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -4,6 +4,11 @@
 
 *   `coef()` allows you to extract the coefficients of an mpoly object (#25, 
     thanks @ggrothendieck).
+    
+*   `deriv()` now allows you to not bring the power down as a multiplier.
+
+*   `normalize_coefficients()` now allows you normalize term coefficients 
+    according to an input norm, defaulting to the Euclidean norm.
 
 
 
diff --git a/R/components.R b/R/components.R
index 0a7795a..2c4b36f 100644
--- a/R/components.R
+++ b/R/components.R
@@ -11,6 +11,9 @@
 #' @param object mpoly object to pass to [coef()]
 #' @param ... In [coef()], additional arguments passed to [print.mpoly()] for
 #'   the names of the resulting vector
+#' @param p an object of class mpoly or mpolyList
+#' @param norm a norm (function) to normalize the coefficients of a polynomial, 
+#'   defaults to the Euclidean norm
 #' @return An object of class mpoly or mpolyList, depending on the context
 #' @name components
 #' @examples
@@ -35,6 +38,18 @@
 #'
 #' homogeneous_components(p)
 #' 
+#' (p <- mp("(x + y)^2"))
+#' normalize_coefficients(p)
+#' norm <- function(v) sqrt(sum(v^2))
+#' norm(coef( normalize_coefficients(p) ))
+#' 
+#' abs_norm <- function(x) sum(abs(x))
+#' normalize_coefficients(p, norm = abs_norm)
+#' 
+#' p <- mp(c("x", "2 y"))
+#' normalize_coefficients(p)
+#' 
+#' 
 
 
 
@@ -174,3 +189,16 @@ coef.mpoly <- function(object, ...) {
 
 
 
+
+
+#' @rdname components
+#' @export
+normalize_coefficients <- function(p, norm = function(x) sqrt(sum(x^2))) {
+  if (is.mpolyList(p)) return( structure(lapply(p, normalize_coefficients), class = "mpolyList") )
+  normalize <- function(x) x / norm(x)
+  c <- normalize(coef(p))
+  for (i in seq_along(p)) p[[i]]["coef"] <- c[i]
+  p
+}
+
+
diff --git a/R/deriv.mpoly.R b/R/deriv.mpoly.R
index 74e0135..9a303f1 100644
--- a/R/deriv.mpoly.R
+++ b/R/deriv.mpoly.R
@@ -6,18 +6,25 @@
 #' @param expr an object of class mpoly
 #' @param var character - the partial derivative desired
 #' @param ... any additional arguments
+#' @param bring_power_down if `FALSE`, x^n -> x^(n-1), not n x^(n-1)
 #' @return An object of class mpoly or mpolyList.
 #' @export
 #' @examples
-#' m <- mp("x y + y z + z^2")
-#' deriv(m, "x")
-#' deriv(m, "y")
-#' deriv(m, "z")
-#' deriv(m, c("x","y","z"))
-#' deriv(m, "a")
-#' is.mpoly(deriv(m, "x"))
-#' is.mpolyList( deriv(m, c("x","y","z")) )
-deriv.mpoly <- function(expr, var, ...){
+#' p <- mp("x y + y z + z^2")
+#' deriv(p, "x")
+#' deriv(p, "y")
+#' deriv(p, "z")
+#' deriv(p, "t")
+#' deriv(p, c("x","y","z"))
+#' 
+#' is.mpoly(deriv(p, "x"))
+#' is.mpolyList( deriv(p, c("x","y","z")) )
+#' 
+#' p <- mp("x^5")
+#' deriv(p, "x")
+#' deriv(p, "x", bring_power_down = FALSE)
+#' 
+deriv.mpoly <- function(expr, var, ..., bring_power_down = TRUE){
 
   # argument checks	
   if (missing(var)) stop("var must be specified, see ?deriv.mpoly", call. = FALSE)
@@ -46,7 +53,7 @@ deriv.mpoly <- function(expr, var, ...){
   	if(length(v) == 1) return(c(coef = 0))
     p <- length(v)
     if(!(var %in% names(v[1:p]))) return(c(coef = 0))
-    v["coef"] <- unname(v[var]) * v["coef"]
+    if (bring_power_down) v["coef"] <- unname(v[var]) * v["coef"]
     v[var] <- v[var] - 1
     v
   })
diff --git a/man/components.Rd b/man/components.Rd
index e4ac4b3..1198d2d 100644
--- a/man/components.Rd
+++ b/man/components.Rd
@@ -11,6 +11,7 @@
 \alias{monomials}
 \alias{exponents}
 \alias{coef.mpoly}
+\alias{normalize_coefficients}
 \title{Polynomial components}
 \usage{
 \method{[}{mpoly}(x, ndx)
@@ -30,6 +31,8 @@ monomials(x, unit = FALSE)
 exponents(x, reduced = FALSE)
 
 \method{coef}{mpoly}(object, ...)
+
+normalize_coefficients(p, norm = function(x) sqrt(sum(x^2)))
 }
 \arguments{
 \item{x}{an object of class mpoly}
@@ -48,6 +51,11 @@ exponents(x, reduced = FALSE)
 
 \item{...}{In \code{\link[=coef]{coef()}}, additional arguments passed to \code{\link[=print.mpoly]{print.mpoly()}} for
 the names of the resulting vector}
+
+\item{p}{an object of class mpoly or mpolyList}
+
+\item{norm}{a norm (function) to normalize the coefficients of a polynomial,
+defaults to the Euclidean norm}
 }
 \value{
 An object of class mpoly or mpolyList, depending on the context
@@ -77,4 +85,16 @@ lapply(exponents(p), is.integer)
 
 homogeneous_components(p)
 
+(p <- mp("(x + y)^2"))
+normalize_coefficients(p)
+norm <- function(v) sqrt(sum(v^2))
+norm(coef( normalize_coefficients(p) ))
+
+abs_norm <- function(x) sum(abs(x))
+normalize_coefficients(p, norm = abs_norm)
+
+p <- mp(c("x", "2 y"))
+normalize_coefficients(p)
+
+
 }
diff --git a/man/deriv.mpoly.Rd b/man/deriv.mpoly.Rd
index 41d32d3..99d1f49 100644
--- a/man/deriv.mpoly.Rd
+++ b/man/deriv.mpoly.Rd
@@ -4,7 +4,7 @@
 \alias{deriv.mpoly}
 \title{Compute partial derivatives of a multivariate polynomial.}
 \usage{
-\method{deriv}{mpoly}(expr, var, ...)
+\method{deriv}{mpoly}(expr, var, ..., bring_power_down = TRUE)
 }
 \arguments{
 \item{expr}{an object of class mpoly}
@@ -12,6 +12,8 @@
 \item{var}{character - the partial derivative desired}
 
 \item{...}{any additional arguments}
+
+\item{bring_power_down}{if \code{FALSE}, x^n -> x^(n-1), not n x^(n-1)}
 }
 \value{
 An object of class mpoly or mpolyList.
@@ -21,12 +23,18 @@ This is a deriv method for mpoly objects.  It does not call the
 \code{\link[stats:deriv]{stats::deriv()}}.
 }
 \examples{
-m <- mp("x y + y z + z^2")
-deriv(m, "x")
-deriv(m, "y")
-deriv(m, "z")
-deriv(m, c("x","y","z"))
-deriv(m, "a")
-is.mpoly(deriv(m, "x"))
-is.mpolyList( deriv(m, c("x","y","z")) )
+p <- mp("x y + y z + z^2")
+deriv(p, "x")
+deriv(p, "y")
+deriv(p, "z")
+deriv(p, "t")
+deriv(p, c("x","y","z"))
+
+is.mpoly(deriv(p, "x"))
+is.mpolyList( deriv(p, c("x","y","z")) )
+
+p <- mp("x^5")
+deriv(p, "x")
+deriv(p, "x", bring_power_down = FALSE)
+
 }
diff --git a/tests/testthat/test-components.R b/tests/testthat/test-components.R
index 5cbcd6a..2cf1eb1 100644
--- a/tests/testthat/test-components.R
+++ b/tests/testthat/test-components.R
@@ -129,3 +129,51 @@ test_that("coef works", {
 
 
 
+
+
+test_that("normalize_coefficients works", {
+  
+  p <- mp("(x + y)^2")
+  
+  expect_equal(
+    normalize_coefficients(p),
+    structure(
+      list(
+        c(x = 2, coef = 0.408248290463863), 
+        c(x = 1, y = 1, coef = 0.816496580927726), 
+        c(y = 2, coef = 0.408248290463863)
+      ), 
+      class = "mpoly"
+    )
+  )
+  
+  abs_norm <- function(x) sum(abs(x))
+  expect_equal(
+    normalize_coefficients(p, norm = abs_norm),
+    structure(
+      list(
+        c(x = 2, coef = 0.25), 
+        c(x = 1, y = 1, coef = 0.5), 
+        c(y = 2, coef = 0.25)
+      ), 
+      class = "mpoly"
+    )
+  )
+  
+  expect_equal(
+    sum(coef(normalize_coefficients(p))^2),
+    1
+  )
+  
+  expect_equal(
+    normalize_coefficients(mp(c("x", "5 y"))),
+    mp(c("x", "y"))
+  )
+  
+  
+  
+  
+})
+
+
+
diff --git a/tests/testthat/test-deriv.R b/tests/testthat/test-deriv.R
index ba7eee0..377a71e 100644
--- a/tests/testthat/test-deriv.R
+++ b/tests/testthat/test-deriv.R
@@ -47,6 +47,21 @@ test_that("vector indeterminates", {
 
 
 
+
+
+test_that("bring_down_power works", {
+  
+  p <- mp("x^5")
+  
+  expect_equal(
+    mp("x^4"),
+    deriv(p, "x", bring_power_down = FALSE)
+  )
+  
+})
+
+
+
 test_that("gradient", {
   
   expect_equal(