Question

Differentiate (t^2 + 2)/(t^4 - 3t^2 + 1)

Answer 1

`y=(t^2 + 2)/(t^4 - 3t^2 + 1) \\ \\y'=((t^2 + 2)/(t^4 - 3t^2 + 1))'= ((t^2+2)'(t^4 - 3t^2 + 1)-(t^2+2)(t^4 - 3t^2 + 1)')/((t^4 - 3t^2 + 1)^2) = \\ \\=(2t(t^4 - 3t^2 + 1)-(t^2+2)(4t^3 - 6t))/((t^4 - 3t^2 + 1)^2) =(2t^5-6t^3+2t-4t^5+6t^3-8t^3+12t)/((t^4 - 3t^2 + 1)^2) = \\ \\=(-2t^5-8t^3+14t)/((t^4 - 3t^2 + 1)^2)`