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Math Help - quotient rule

  1. #1
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    quotient rule

    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

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

    if I use the product rule after making it a product it is pretty easy to obtain \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
    \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}

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

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

    .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.
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  2. #2
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    Re: quotient rule

    To check your answers, you can go to WolframAlpha.com and after getting a solution, click on Step-by-step Solution: link. Yes, your solution is correct.
    Thanks from Jonroberts74
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  3. #3
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    Re: quotient rule

    Hey Jonroberts74.

    Your working is very good.

    Just for future notice, if you can't get anyone to check your work, you should use something like Maple or Mathematica to check your work.
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