Turunan dan Diferensiasi

Nama : Muhammad Hafidlul Qolbi

NIM : 220605110063

Kelas : C

Mata Kuliah : Kalkulus

Dosen Pengampuh : Prof. Dr. Suhartono, M.Kom

Jurusan : Teknik Informatika

Lembaga : Universitas Islam Negeri 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

## 
## Attaching package: 'mosaicCalc'

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

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

## [1] 2

library(mosaicCalc)
my_function <- function(x)(
  return(5 * x^5)
)
my_function(2)

## [1] 160

g <- D(5*x^5 ~ x)
g

## function (x) 
## 25 * x^4

g <- D(my_function(x) ~ x)
g(2)

## [1] 400

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)))

Latihan nomer 1

1. turunan dari fungsi g(x)

library(mosaicCalc)
g <- D(3 * x ^ 2 - 2*x + 4 ~ x)
g(-6)

## [1] -38

g(-4)

## [1] -26

g(-3)

## [1] -20

g(-2)

## [1] -14

g (0)

## [1] -2

g(2)

## [1] 10

g(3)

## [1] 16

g(4)

## [1] 22

g(6)

## [1] 34

2. membuat grafik fungsi g(x)

slice_plot(3 * x ^ 2 - 2*x + 4 ~ x, domain (x = range(40,-40)))

Latihan 2

1. Mencari Turunan

library(mosaicCalc)
g <- D(5 * exp(0.2 * x) ~ x)
g(-5)

## [1] 0.3678794

g(-2)

## [1] 0.67032

g(-1)

## [1] 0.8187308

g(0)

## [1] 1

g(1)

## [1] 1.221403

g(2)

## [1] 1.491825

g(5)

## [1] 2.718282

2. Membuat Grafik

slice_plot(5 * exp(0.2 * x) ~ x, domain (x = range(0,3)))