Question

How do you derive `y = -1/(1+x^2)+1/x^2` using the quotient rule?

Answer 1

`(-4x^3 -2x)/(x^4 (1+x^2)^2)`

Explanation:

To simplify the matters, add both the fractions = `1/(x^2 (1+x^2))` = `1/((x^4 +x^2 )`

Now use quotient rule y' = `(0(x^2+x^4)- 1(4x^3 +2x))/(x^4 (1+x^2)^2)`

=`(-4x^3 -2x)/(x^4 (1+x^2)^2)`