Math Problems 9/27/26

Question 1

A formula uses \(f(x) = \tan^{-1} (\frac{3}{2}x)\). What is \(f'(x)\)?

# install.packages("Deriv")
library(Deriv)
f <- function(x) {
  atan(1.5 * x)
}
f_prime <- Deriv(f)
f_prime

## function (x) 
## 1.5/((1.5 * x)^2 + 1)

Question 2

Write 1,860,002 in words.

# install.packages("english")
library(english)

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

words(1860002)

## [1] "one million eight hundred sixty thousand two"

Question 3

Differentiate \(g(x) = \sin^2(x)\).

# install.packages("Deriv")
library(Deriv)
g <- function(x) {
  (sin(x))^2
}
g_prime <- Deriv(g)
g_prime

## function (x) 
## 2 * (cos(x) * sin(x))