Find derivatives of the functions defined as follows.y=(t^2 e^(2t))/(t+e^(3t))

Question

Find derivatives of the functions defined as follows.y=(t^2 e^(2t))/(t+e^(3t))

shadsiei 2020-12-28 Answered

Find derivatives of the functions defined as follows. $y = (t^{2} e^{(2 t)}) / (t + e^{(3 t)})$

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Expert Answer

Alara Mccarthy

Answered 2020-12-29 Author has 85 answers

$d y / d t = ((t + e^{(3 t)}) (2 t^{2} e^{(2 t)} + 2 t e^{(2 t)}) - (t^{2} e^{(2 t)}) (1 + 3 e^{(3 t)})) / ((t + e^{(3 t)})^{2})$
$= (2 t^{3} e^{(2 t)} + 2 t^{2} e^{(2 t)} + 2 t^{2} e^{(5 t)} + 2 t e^{(5 t)} - t^{2} e^{(2 t)} + 3 t^{2} e^{(5 t)}) / ((t + e^{(3 t)})^{2})$
$= ((5 t^{2} + 2 t) e^{(5 t)} + (2 t^{3} + t^{2}) e^{(2 t)}) / ((t + e^{(3 t)})^{2})$

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