f(t)=(t)/((t^2)-2)?

1 ⤊

Differentiate the function.

2007-06-20 01:30:30 · 3 answers · asked by capslock077 1 in Science & Mathematics ➔ Mathematics

3 answers

Use the Quotient rule:

f' = { (t^2-2)*t' - t*(t^2-2)' } / (t^2-2)^2
f' = (t^2 - 2 - 2t^2) / (t^2 - 2)^2
f' = (-2 - t^2) / (t^2 - 2)^2

2007-06-20 01:34:58 · answer #1 · answered by McFate 7 · 1⤊ 0⤋

.use the quotient rule
d(u/v)/dt =(vdu/dt - udv/dt)/v^2
so
d(t/((t^2)-2))/dt
= ( ((t^2)-2)*dt/dt - t*d((t^2)-2)/dt ) / ((t^2)-2))^2
= ( (t^2)-2)*1 - t*(2t) ) / ((t^2)-2))^2
= ( (t^2) -2 - 2(t^2) ) / ((t^2)-2))^2
= - ( (t^2)+2 ) / ((t^2)-2)^2

the end

2007-06-20 08:33:52 · answer #2 · answered by The Wolf 6 · 0⤊ 0⤋

f'(t)=(t^2-2)-{t*(2t)}/(t^2-2)^2
= (-t^2 -2)/ (t^2-2)^2

2007-06-20 08:39:46 · answer #3 · answered by NIRAJ 2 · 0⤊ 0⤋