Question

найдите производную
$\frac{x - 2}{{3x}^{2} - 1 }$

Answer 1

$( \frac{x - 2}{{3x}^{2} - 1 } )' = \frac{(x - 2)'*({3x}^{2}-1)-(x - 2)*({3x}^{2}-1)'}{{(3x}^{2}-1)^2} = \\ \\ = \frac{({3x}^{2}-1)-(x - 2)*{6x}}{{(3x}^{2}-1)^2} = \frac{{3x}^{2}-1-6 x^{2}+12x}{{(3x}^{2}-1)^2} = \frac{{-3x}^{2}+12x-1}{{(3x}^{2}-1)^2}$