Problem

Compute the differential dy of \(y=x^2+3x-5\)

Christian’s Response:

The differential dy or derivative of y, can be calculated with the power rule of differentiation. Using this rule, we can identify the dy:

\[ y'(x)=(d/dx)(x^2+3x-5)\\ =(d/dx)x^2 + (d/dx)3x - (d/dx)5\\ =2x + 3(1) - 0\\ =2x + 3 \] Bonus: Now that I have solved for differential dy, I will solve for when x=2 in code.

# creates y(x)
y <- function(x) {
  x^2 + 3*x - 5
}

# define dy(x)
dy <- function(x) {
  2*x + 3
}

# create variable 2
x <-2

cat("y(", x, ") =", y(x), "\n")
## y( 2 ) = 5
cat("dy(", x, ") =", dy(x), "\n")
## dy( 2 ) = 7

The differential dy of y = x^2 + 3x -5 is dy = 2x +3. When x=2, dy=7