I always find it much easier to put a rational function into a product when I need to differentiate but I am trying to work on using the quotient rule.

the function is

$\displaystyle \frac{.1t}{(t+3)^2}$

if I use the product rule after making it a product it is pretty easy to obtain $\displaystyle \frac{.3-.1t}{(t+3)^3}$

but when I try to use the quotient rule it isn't as simple

I think I have the work correct in this

$\displaystyle \frac{d}{dt}\frac{.1t}{(t+3)^2} \Rightarrow .1\frac{d}{dt}\frac{t}{(t+3)^2} \Rightarrow .1\frac{1(t+3)^2 - 2(t+3)^1(t)}{((t+3)^2)^2} $

$\displaystyle .1[\frac{(t+3)^2}{(t+3)^4} - \frac{2t(t+3)}{(t+3)^4}]$

$\displaystyle .1[\frac{1}{(t+3)^2} - \frac{2t}{(t+3)^3]}$

$\displaystyle .1[\frac{(t+3)-2t}{(t+3)^3}] \Rightarrow \frac{.3-.1t}{(t+3)^3}$

Thanks! I know it seems like a pointless post but I just want to make sure my sequence is correct.