Find f'(a)

Question

Find f'(a)

abbles · Answer

$$f(t) = \frac{ 2t+1 }{ t+3 }$$

welshfella · Answer

first find f'(t)  
use the Quotient rule.

abbles · Answer

I haven't learned any of the rules yet, my teacher said to use the definition of the derivative.. she said we had to show all of our work to get credit :3

abbles · Answer

I haven't done any with fractions like this yet though...

agent0smith · Answer

http://archives.math.utk.edu/visual.calculus/2/definition.12/eq1.gif $$\Large f'(x) = \lim_{h \rightarrow 0} \frac {\frac{ 2(t+h)+1 }{ (t+h)+3 } - \frac{ 2t+1 }{ t+3 } }{ h }$$Now we gotta simplify some fractions and get common denoms.

abbles · Answer

Perfect, thank you!  I can handle it from here.  Just couldn't figure out how to set it up...

agent0smith · Answer

Okay, let me know if you get stuck, but it's not too bad from there, just getting common denoms

abbles · Answer

I keep messing up :/
$$\frac{ (t+3)(2t+2h+1)-(2t+1)(t+h+3) }{ h(t+3)(t+h+3) }$$
Does this look right so far?

abbles · Answer

Never mind, I just got it!  Ahh :D
Long problems.