Question

Cual es la derivada de
3x2-1
____
2x3+x

Answer 1

Solución
$= d( \frac{3 {x}^{2} - 1}{2 {x}^{3 } + x } ) \\ = \frac{(6x)(2 {x}^{3}- 1) - (6 {x}^{2} + 1)(3 {x}^{2} - 1)}{ {(2 {x}^{3} + x) }^{2} } \\ = \frac{12 {x}^{4} - 6x - 18 {x}^{4}+ 6 {x}^{2} - 3 {x}^{2} + 1 }{ {(2 {x}^{3} + x)}^{2} } \\ = \frac{ - 6 {x}^{4} + 3 {x}^{2} - 6x + 1 }{{(2 {x}^{3} + x)}^{2}}$