anonymous
  • anonymous
Can someone help me finish this derivative, using the first principle rule. [picture attached]
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
|dw:1371172930181:dw|
anonymous
  • anonymous
it's wrong btw

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Callisto
  • Callisto
\[f(t) = \frac{-2t}{t+3}\]\[f'(t) = \lim_{h \rightarrow 0}\frac{f(t+h)-f(t)}{h}\] \[f(t+h) =\frac{-2(t+h)}{(t+h)+3}\] Does that help?
anonymous
  • anonymous
is what i have done so far right ? (there's an attachment)
whpalmer4
  • whpalmer4
\[\lim_{h->0}\frac{1}{h}*[\frac{-6h-6t-2ht-2t^2}{(t+3)(t+h+3)}+\frac{6t+2ht+2t^2}{(t+3)(t+h+3)}]\] is what you get after a bit of the algebraic dust settles...
anonymous
  • anonymous
that's exactly what im getting but i'm not understanding why my answer key shows \[\frac{ 5t-2 }{ 2(5t-1)^{\frac{ 3 }{ 2 }} }\]
Callisto
  • Callisto
Double check the answer key?
anonymous
  • anonymous
I have, maybe it's just wrong :S
whpalmer4
  • whpalmer4
That's the right answer, if the problem is to find the derivative of \[\frac{t}{\sqrt{5t-1}}\]

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