Question

What is the derivative of `(-x^2+5)/(x^2+5)^2`?

Answer 1

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

Explanation:

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

`y' = (-2x(x^4 + 10x +25) - 4x(-x^4 - cancel(5x^2) +cancel(5x^2) + 25))/((x^2 +5)^4`

`y' = (-2x^5 - 20x^2 -50x + 4x^5 - 100x)/((x^2 +5)^4`

`y' = (2x^5 - 20x^2 - 150x)/((x^2 +5)^4`