Question

How do you use the quotient rule to differentiate `(4x − 2) / (x^2 + 1)`?

Answer 1

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

Explanation:

The differential coefficient of a fraction is given by (Denominator * Diff. Coeff. of Numerator - Numerator * Diff. Coeff. of Denominator) / Denominator^2
Here DC of Denominator = 2x
and DC of Numerator = 4
Substituting we get
`((x^2 + 1) * 4 - (4x - 2) * 2x) / (x^2 + 1)^2`
Expanding we get `(4*x^2 + 4 - 8*x^2 + 4*x) / (x^4 + 2*x^2 + 1)`
Simplifying, we get
`(-4*x^2 + 4*x + 4) / (x^4 + 2*x^2 + 1)`
ie `4*(-x^2 +x + 1) / (x^4 + 2*x^2 + 1)`

Hope it is clear