Question

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

Answer 1

You may use the quotient rule

Answer 2

t^2+2/t^4-3t^2+1

Answer 3

\[y'=\frac{(t^4-3t^2+1)(2t)-(t^2+2)(4t^3-6t)}{(t^4-3t^2+1)^2}\]

Answer 4

Probably need to do some algebra and clean it up a bit.

Answer 5

right i did that but i got [2t(-t^4 - 7t^2 + 7)]/[(t^4 - 3t^3 + 1)^2], which is incorrect apparently

Answer 6

so any ideas? i've gone over and over it can't figure out where the issue is

Answer 7

\[y'=\frac{(t^4-3t^2+1)(2t)-(t^2+2)(4t^3-6t)}{(t^4-3t^2+1)^2} = \frac {2t^5 - 6t^3 + 2t - 4t^5+ 6t^3 - 8t^3 + 12t}{(t^4 - 3t^2 + 1)^2}\]\[y' = \frac {-2t^5 - 8t^3 + 14t}{(t^4 - 3t^2 + 1)^2} = \frac {-2t(t^4 + 4t^2 - 7)}{(t^4 - 3t^2 + 1)^2}\]

Answer 8

You just have to be really careful with the signs, it gets messy...

Answer 9

your middle term in the numerator should -4t^2 instead of -7t^2. try expanding again and be very careful with signs...