Rangkuman 7

Kalkulus by Prof. Dr. SUHARTONO, M.Kom || Izza Syahri Muharram _ 220605110073 || Teknik Informatika || UIN Maulana Malik Ibrahim Malang

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library(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

library(mosaicCalc)

## Loading required package: mosaicCore

## 
## Attaching package: 'mosaicCore'

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

## 
## Attaching package: 'mosaicCalc'

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

g <- D(x^2 ~ x)
g(1)

## [1] 2

input = ekspresi menggunakan ~ notasi contoh x^2~x atau sin (x^2)~x sisi kiri adalah ekspresi matematika yang akan dievaluasi menjadi angka ketika numerik tersedia tersedia untuk semua besaran yang dirujuk. sisi kanan ~ adalah variable yang akan diambil turunannya.

//RUMUS DAN SELISIH NUMERIK

h <- D(sin(abs(x - 3) ) ~ x)
h

## function (x) 
## {
##     .e1 <- x - 3
##     cos(abs(.e1)) * sign(.e1)
## }

Untuk ekspresi lainnya D() akan mengembalikan fungsi yang didasarkan pada perasaan numerik ke turunan

//PARAMETER SIMBOLIK

library(mosaicCalc)
s2 <- D(A  * sin(2 * pi * t / P) + C ~ t)
s2( t=3, A=2, P=10, C=4 )

## [1] -0.3883222

slice_plot(s2(t, A=2, P=10, C=4) ~ t, 
           domain(t=range(0,20)))

Menyertakan parameter simbolik dalam ekspresi yang dimasukkan ke D(), misal dalam hal ini A,P, dan C akan diubah menjadi argumen ke S2(). fungsi s2 yang dibuat akan bekerja seperti fungsi matematika lainnya.

// DERIVATIF PARSIAL /Turunan kedua menggunakan D() operator dua kali untuk menemukan turunan kedua.

df <- D(sin(x) ~ x)
ddf <- D(df(x) ~ x)

findiff <- function(f, x, h, method=NULL){
  if(is.null(method)){
    warning("please select a method")
  }else{
    if(method == "forward"){
      return((f(x+h)-f(x))/h)
    }else if(method=="backward"){
      return((f(x)-f(x-h))/h)
    }else if(method=="central"){
      return((f(x+h)-f(x-h))/(2*h))
    }else{
      warning("you can use method: forward, bacward, or central")
    }
  }
}

Latihan 1. Jika ƒ(x) = 3 (x^8) − 5(x^6) + x*4 − x + 11, maka turunan dari f(x) di x = 3 adalah

findiff(function(x)
3*(x^8) + 5*(x^6) + x*4-x + 11, x=4, h=0.05,
  method="central")

## [1] 424385.1

2. y = x3 + 3x^2 maka turunan dari f(x) di x = 3 adalah

findiff(function(x)
3*x + 3*(x^2) + x , x=3, h=0.05,
  method="central")

## [1] 22

3. y = 3(x^4) + 2(x^2) + 2*x dengan dimisalkan dengan a= 2, x= 1, h= 0.05.

findiff(function(x)
3*(x^4) + 2*(x^2) + 2*x, x=1, h=0.05,
  method="central")

## [1] 18.03

Daftar pustaka https://dtkaplan.github.io/RforCalculus/derivatives-and-differentiation.html#partial-derivatives https://rumuspintar.com/turunan/#:text=Kesimpulan-,Definisi%20Turunan,suatu%20fungsi%20disebut%20sebagai%20diferensiasi