Data 605 - Disussion #13

library(Deriv)

Calculus - Chapter 4: Exerise #20

Computer the differential \(dy\)

\(Given:\) \(y = (2x + \sin x)^2\)

fx1 <- function(x){
    (2*x + sin(x))^2
}
fx1prime <- Deriv(fx1)
fx1prime

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

\(dy = f'((2x + \sin x)^2)dx\)

\(= 2(2x + \sin x) \cdot (2 + \cos x)\)

\(= 8x + 4\sin x + 4x\cos x + 2\sin x \cos x\)

\(dy = 8x + 4\sin x + 4x\cos x + \sin(2x)\)