Question

Differentiate the following w.r.t.x. :

y = `(x^2 + 3)/(x^2 - 5)`

Answer 1

Let y = `(x^2 + 3)/(x^2 - 5)`

∴ `("d"y)/("d"x) = "d"/("d"x) [(x^2 + 3)/(x^2 - 5)]`

= `((x^2 - 5) "d"/("d"x) (x^2 + 3) - (x^2 + 3) "d"/("d"x) (x^2 - 5))/(x^2 - 5)^2`

= `((x^2 - 5)(2x + 0) - (x^2 + 3)(2x - 0))/(x^2 - 5)^2`

= `(2x[(x^2 - 5) - (x^2 + 3)])/(x^2 - 5)^2`

= `(- 16x)/(x^2 - 5)^2`