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Numerade Educator

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Problem 22 Easy Difficulty

Differentiate.

$ V(t) = \frac {4 + 1}{te^t} $

Answer

$\frac{\left.-( t^{2}+4 t+4\right) e^{-t}}{t^{2}}$

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Video Transcript

it's clear. So when you read here, So, yeah, we're gonna fund that derivative in terms of tea. So I wrote it a different way. I wrote it T plus four, and I put e in the numerator. It just becomes equal to D over d t 30 plus four e to the t you to the negative t terms T minus T plus or eat the negative t d over DT of tea. Fall over Tea Square. Then we've simplify this when we got t negative d over DT For tea comes T plus four. Eat the negative T plus one plus zero eat to the negative T minus T plus four e to the negative T crawl over Teeth Square. This becomes equal to t terms e to the negative T minus T plus four. Eat the negative T minus T plus four. Eat the negative T while over he's square, you simplify to get T square plus 14th plus four plus four times E to the negative t well over a T square