Could someone help me solve this easy derivative? ...i just need to confirm my answer?

Question

what is the derivative of this?

t/(t^(2) +1)

is it (-t^(2) +1)/ (t^(2) +1)^2?

are we able to simplify that any further?

Answer 1

f (t) = t / (t ² + 1)
Use quotient rule:-
f ' (t) = ( (t ² + 1)(1) - (t) (2t) ) / (t ² + 1) ²
f ' (t) = ( t ² + 1 - 2 t ² ) / (t ² + 1) ²
f ' (t) = ( 1 - t ² ) / (t ² + 1) ²

It seems we agree!

Answer 2

y = t / (t² +1) . . . . this is a fraction
y ' = [ (t² +1) - t (2 t) ] / (t² +1)²
y ' = (- t² +1 ) / (t² +1) ²

Answer 3

you are absolutely correct.....no need to simplify further