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Numerade Educator

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Problem 15 Easy Difficulty

Differentiate.

$ y = \frac {t^3 + 3t}{t^2 - 4t + 3} $

Answer

$\frac{t^{4}-8 t^{3}+6 t^{2}+9}{\left(t^{2}-4 t+3\right)^{2}}$

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Video Transcript

It's clear, so inhumane here. So we're gonna differentiate this in terms of tea. We got t cute plus three tea over T Square minus 40 plus three just becomes equal to D over DT T Q plus three p comes T Square minus 40 plus three minus three Q plus three T terms de over de ti oh, teeth square minus 40 plus three. All over he square minus 40 plus three squared. Can we get three T Square plus three times one comes T square minus 40 plus three minus two tea minus or times one plus Cyril Terms T Acute plus three t all over T square minus 40 plus three square. This becomes equal to T square T to the fourth minus a T cubed plus 60 square less nine over P square minus 40 plus three where