Question

derivative of (1-t)(1+t^2)^-1

Answer 1

do you know the product rule for taking the derivative of two expressions that are multiplied?

Answer 2

do you know this method ? u/v=u'v-v'u/v^2 ?

Answer 3

phi i think the division rule is simpler for him since the 2nd product is ^-1 in which simply you can put it in the deniminator

Answer 4

i do know the product rule, i was just getting lost in the middle of the madness

Answer 5

let u = (1-t)
and v= (1+t^2)^-1

du/dt = -1
dv/dt uses the exponent rule and the chain rule:
\[ \frac{d}{dt}\left( 1+t^2\right)^{-1} = -1 \cdot \left( 1+t^2\right)^{-1-1} \frac{d}{dt}\left( 1+t^2\right)\]
can you finish finding dv/dt ?
then put the pieces together
d(u v) = u dv + v du