Need help finding a derivative..

[hank]

I'm close, but I'm missing a detail somewhere..

find d/dt of: (4-t^2) / (t^2 + 4)^2.

= [(t^2 + 4)^2(-2t) - [(4 - t^2)(4t)(t^2 + 4)] / [t^2 + 4]^4

=[-2t(t^2 + 4)^2 - (4t(4 - t^2)(t^2 + 4))] / [t^2 + 4]^4

= [-2t(t^2 + 4)(t^2 + 4 + 2(4 - t^2))] / [t^2 + 4]^4

= [-2t(t^2 + 4 + 8 - 2t^2)]/[t^2 + 4]^3

= [-2t(12 - t^2)] / [t^2 + 4]^3

This is where I get stuck. The book says the answer is:

2t/(t^2 + 4)^2

Which implies I need to pull a (t^2 + 4) out of the numerator somehow to cancel one out of the denominator, but I can't see it.

What am I missing here?

 

[galactus]

If you have the correct problem:

\(\displaystyle \L\\\frac{d}{dx}\left[\frac{4-t^{2}}{(t^{2}+4)^{2}}\right]=\frac{2t(t^{2}-12)}{(t^{2}+4)^{3}}\)

Then you are correct. The book has a typo.

The answer the book has would be OK if you were differentiating

\(\displaystyle \L\\\frac{-1}{t^{2}+4}\)

 

[hank]

Ya, that's what I thought.

I went back and integrated and it didn't make sense.

Stupid book. I've lost more time to typos than I can count.

Thanks.