Question

Otro ejercicio:
$\frac{d}{dt} ( \frac{5t}{1 + 2t {}^{2} } )$

Answer 1

$\frac{d}{dt} ( \frac{5t}{1 + 2 {t}^{2} } ) = \\ \frac{( \frac{d}{dt} (5t))(1 + 2 {t}^{2} ) - (5t)( \frac{d}{dt} (1 + 2 {t}^{2})) }{ {(1 + 2 {t}^{2}) }^{2} } \\ = \frac{5(1 + 2 {t}^{2} ) - 5t(4t)}{ {(1 + 2 {t}^{2}) }^{2} } \\ = \frac{5 + 10 {t}^{2} - 20 {t}^{2} }{ {(1 + 2 {t}^{2}) }^{2} } \\ = \frac{5 - 10 {t}^{2} }{ {(1 + 2 {t}^{2}) }^{2} }$