Math Problems 8/4/26

Question 1

If \(f(x) = x \ln(x)\), what is \(f'(x)\)?

# install.packages("Deriv")
library(Deriv)
f <- function(x) {
  x * log(x)
}
f_prime <- Deriv(f)
f_prime

## function (x) 
## 1 + log(x)

Question 2

Consider the list of numbers: \([41,43,47,49]\). Which number is composite?

# install.packages(c("comprehenr","pracma"))
library(comprehenr)

## Warning: package 'comprehenr' was built under R version 4.5.2

library(pracma)
answer <- to_vec(for (x in c(41,43,47,49)) if (!isprime(x)) x)
cat("The number that is composite is:",answer,"\n")

## The number that is composite is: 49