Find out the answer to "Find derivatives of the functions defined as follows...."

College
Calculus and Analysis
Differential Calculus
Derivatives

shadsiei

Answered question

2020-12-28

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

Answer & Explanation

Alara Mccarthy

Skilled2020-12-29Added 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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