Question

otro:
$\frac{d}{dy} ( \frac{y {}^{3} - 8 }{y {}^{3} + 8} )$

Answer 1

$\frac{d}{dy} ( \frac{ {y}^{3} - 8 }{ {y}^{3} + 8 } )$
Ocupas la derivación de una división, quedaría:

$\frac{(3 {y}^{2})( {y}^{3} + 8) - ( {y}^{3} - 8)(3 {y}^{2}) }{ {( {y}^{3} + 8)}^{2} } \\ = \frac{3 {y}^{5} + 24 {y}^{2} - 3 {y}^{5} + 24 {y}^{2} }{ { ({y}^{3} + 8) }^{2} } \\ = \frac{48 {y}^{2} }{ { ({y}^{3} + 8)}^{2} }$