Deriv package quotient output interpretation

Question

I used the deriv package to calculate a derivative, but the output after a division really puzzles me.

Here is my function and outcome:

testFunction <- function(x) x/(x^2+1)

Deriv(testFunction)

function (x) 
{   
  .e1 <- x^2
  .e2 <- 1 + .e1
  (1 - 2 * (.e1/.e2))/.e2
}

I know the solution is supposed to be (1-X^2)/(X^2+1)^2, but I don't understand the output with .e1 and .e2 that R gives me.

Answer 1

What do you not understand ?

(1 - 2 * (.e1/.e2))/.e2 = (1 - 2x²/(1+x²))/(1+x²)
= ((1+x² - 2x²)/(1+x²))/(1+x²)
= (1-x²)/(1+x²)²

which is exactly the result you mention.