chapter7

Nama : Ahmad Fadhli Dzilikrom Nim : 220605110078

Chapter 7 Derivatif & diferensiasi

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

g(3.5)

## [1] 7

7.1 rumus dan selisih numerik

g

## function (x) 
## 2 * x
## <bytecode: 0x000001949c537388>

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

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

7.2 Parameter Simbolis

s2 <- D(A  * sin(2 * pi * t / P) + C ~ t)

s2

## function (t, A, C, P) 
## (2 * A * pi * cos((2 * pi * t)/P))/P

s2

## function (t, A, C, P) 
## (2 * A * pi * cos((2 * pi * t)/P))/P

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)))

7.3 Derivatif Parsial

7.3.1 Turunan kedua

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

another.ddf <- D(sin(x) ~ x & x)

7.3.2 Latihan

7.3.2.1 Latihan 1 7.3.2.2 Latihan 2 7.3.2.3 Latihan 3 7.3.2.4 Latihan 4

D(fred^2 ~ ginger)

## function (fred, ginger) 
## 0

7.3.2.5 Latihan 5 7.3.2.6 Latihan 6 7.3.2.7 Latihan 7

pxy = D(x * sin(y) ~ x & y)
pyx = D(x * sin(y) ~ y & x)