Question

I need help on differentiate. I know to use quotient rule, but I can't get the correct answer? -2t^5-4t^3+10/(t^4-3t^3+2)^2 is what i got?

y =
t^2 + 1
divided by
t^4 − 3t^2 + 2

Answer 1

numerator was my attempt to simplify, i originally got 2t(t^4-3t^2+2)-(t^2+1)(4t^3-6t)

Answer 2

Hmm your numerator looks good.
I don't think you should try to simplify this one +_+ Ew..

Answer 3

Oh I guess you get some nice cancellations n stuff if you do.. grr

Answer 4

okay thank you zepdrix ill just let it go :)

Answer 5

\[y=\frac{t^2+1}{t^4-3t^2+2}\]
So
\[\begin{align*}y'&=\frac{\left(t^4-3t^2+2\right)(2t)-\left(t^2+1\right)\left(4t^3-6t\right)}{\left(t^4-3t^2+2\right)^2}\\
&=\frac{2t\left[\left(t^4-3t^2+2\right)-\left(t^2+1\right)\left(2t^2-3\right)\right]}{\left(t^4-3t^2+2\right)^2}\\
&=\frac{2t\left[\left(t^4-3t^2+2\right)-\left(2t^4-t^2-3\right)\right]}{\left(t^4-3t^2+2\right)^2}\\
&=\frac{2t\left[-t^4-2t^2+5\right]}{\left(t^4-3t^2+2\right)^2}\\
&=\frac{-2t\left[t^4+2t^2-5\right]}{\left(t^4-3t^2+2\right)^2}\end{align*}\]
is what I'm getting...