Differentiation

library(mosaicCalc)

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Differentiation adalah Proses membangun turunan suatu fungsi. Fungsi yang diberikan sering kali menggambarkan hubungan antara dua besaran atau variabel yang saling terkait. Turunan memungkinkan kita untuk mengukur tingkat perubahan fungsi tersebut terhadap satu variabel terhadap yang lainnya.

Secara formal, jika kita memiliki fungsif(x), turunan dari fungsi ini, sering disimbolkan sebagai f’(x) atau df/dx, menghasilkan fungsi baru yang menunjukkan laju perubahan nilai f(x) terhadap x.

# Memuat library yang diperlukan
library(ggplot2)

# Fungsi yang ingin kita hitung turunannya
f <- function(x) {
  return(x^2 - 8)
}

# Menghitung turunan dari fungsi tersebut
df <- D(expression(x^2 - 8), "x")

# Membuat rentang nilai x
x_vals <- seq(-5, 5, by = 0.1)

# Menghitung nilai y dari fungsi dan turunannya
y_vals <- sapply(x_vals, f)
dy_vals <- sapply(x_vals, function(x) eval(df))

# Membuat dataframe dari vektor
df <- data.frame(x = x_vals, y = y_vals, dy = dy_vals)

# Membuat plot fungsi dan turunannya
ggplot(df, aes(x = x)) +
  geom_line(aes(y = y), color = "blue") +
  geom_line(aes(y = dy), color = "red") +
  ggtitle("Function and Its Derivative") +
  xlab("x") +
  ylab("y") +
  scale_color_manual(values = c("blue", "red"), labels = c("Function", "Derivative")) +
  theme(legend.position = c(0.8, 0.9))