Question

Найдите производную функции:
1)y=(2x^2+3x)/((x^2)-4);
2)y=(x-1)/(√x)

Answer 1

Ответ:

$1)y = \frac{(2 {x}^{2} + 3x)}{(( {x}^{2}) - 4) } \\ y = \frac{(2 {x}^{2} + 3x)( {x}^{2} - 4) - (2 {x}^{2} + 3x) \times ( {x}^{2} - 4)}{( {x}^{2} - 4 {)}^{2} } \\ y = \frac{(2 \times 2x + 3)( {x}^{2} - 4) - (2 {x}^{2} + 3x) \times 2x }{( {x}^{2} - 4 {)}^{2} } \\ y = \frac{ - 3 {x}^{2} - 16x - 12 }{( {x}^{2} - 4 {)}^{2} } \\ 2)y = \frac{(x - 1)}{( \sqrt{x}) } \\ y = \frac{(x - 1) \times \sqrt{x} - (x - 1) \times ( \sqrt{x}) }{ \sqrt{x} {}^{2} } \\ y = \frac{1 \sqrt{x} - (x - 1) \times \frac{1}{2 \sqrt{x} } }{ \sqrt{x} {}^{2} } \\ y = \frac{x + 1}{2x \sqrt{x} }$