Question

......,....
..........​

Answer 1

1)

$y = {x}^{5} - 3 {x}^{3} + {x}^{2} - 1 \\ y' = 5 {x}^{5 - 1} - 3 \times 3 {x}^{3 - 1} + 2 {x}^{2 - 1} = \\ 5 {x}^{4} - 9 {x}^{2} + 2x = \\ x(5 {x}^{3} - 9x + 2)$

2)

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