Diferensiasi simbolis

Nama : Muhammad Nur Ramadhan

NIM : 230605110077

KELAS : C KALKULUS

DOSEN PENGAMPU : Prof. Dr. SUHARTONO, M.Kom

LEMBAGA : UIN MAULANA MALIK IBRAHIM MALANG

library(mosaicCalc)

## Loading required package: mosaic

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally

## The following object is masked from 'package:Matrix':
## 
##     mean

## The following object is masked from 'package:ggplot2':
## 
##     stat

## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum

## Loading required package: mosaicCore

## 
## Attaching package: 'mosaicCore'

## The following objects are masked from 'package:dplyr':
## 
##     count, tally

## The legacy packages maptools, rgdal, and rgeos, underpinning the sp package,
## which was just loaded, will retire in October 2023.
## Please refer to R-spatial evolution reports for details, especially
## https://r-spatial.org/r/2023/05/15/evolution4.html.
## It may be desirable to make the sf package available;
## package maintainers should consider adding sf to Suggests:.
## The sp package is now running under evolution status 2
##      (status 2 uses the sf package in place of rgdal)

## 
## Attaching package: 'mosaicCalc'

## The following object is masked from 'package:stats':
## 
##     D

Fungsi R/mosaik D()mengambil rumus suatu fungsi dan menghasilkan turunannya. Ini menggunakan jenis ekspresi tilde yang sama yang digunakan oleh makeFun()atau contour_plot()atau alat R/mosaik lainnya. Contohnya,

jika mau, Anda dapat menggunakannya makeFun()untuk mendefinisikan suatu fungsi, lalu menyerahkan fungsi tersebut D()untuk diferensiasi.

D(t * sin(t) ~ t)

## function (t) 
## sin(t) + t * cos(t)

## function (t) 
## sin(t) + t * cos(t)

Di sisi kanan ekspresi tilde diserahkan ke D()nama yang berkaitan dengan masukan. Hal ini mirip dengan ekspresi tilde yang digunakan dalam pembuatan plot, yang memberi nama masukan yang membentuk domain grafis. Namun hal ini berbeda dengan ekspresi gelombang di makeFun(), yang mana sisi kanan menentukan urutan kemunculan input yang Anda inginkan.

myf <- makeFun(sqrt(y * pnorm(1 + x^2, mean=2, sd=3)) ~ x & y)
dx_myf <- D(myf(x, y) ~ x, y=3)
dx_myf

## function (x, y = 3) 
## {
##     .e1 <- 1 + x^2
##     x * y * dnorm(.e1, 2, 3)/sqrt(y * pnorm(.e1, mean = 2, sd = 3))
## }

## function (x, y = 3) 
## {
##     .e1 <- 1 + x^2
##     x * y * dnorm(.e1, 2, 3)/sqrt(y * pnorm(.e1, mean = 2, sd = 3))
## }

D(sin(t) ~ t)

## function (t) 
## cos(t)

## function (t) 
## cos(t)
D(log(x) ~ x)

## function (x) 
## 1/x

## function (x) 
## 1/x
D(exp(x) ~ x)

## function (x) 
## exp(x)

## function (x) 
## exp(x)
D(x^2 ~ x)

## function (x) 
## 2 * x

## function (x) 
## 2 * x