Quotient Rule proof: toy w/ parachute thrown into air; height H(t) = (4t^{2/3})/(t^2+1)

[Astronomer_X]

Here is the question:

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Here is my attempt:

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QR2 hosted at ImgBB

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I had this exact same question in some work about two weeks ago, and got a teacher to try explain it. Their explanation wasn't very clear to me, which is really shown by the fact that I got to the exact same point now as before, which really shows my lack of grasp as to how I need to approach this kind of quotient rule question. I think there's something to do with manipulating fractions which is catching me off, but I honestly am not certain. It's kind of frustrating at this point, and I figured I would ask here to see if anyone here knows about what to do?

 

[Dr.Peterson]

You multiplied a numerator on the second page by 3t^{-1/3} when it should have been 3t^{1/3}, namely the denominator of the first fraction.

Fix that, and there will be very little work left to do.