Question

Знайдіть похідну функції

Answer 1

$f(x) = \frac{x - 7}{ {x}^{2} - 3 } \\ f'(x) = \frac{(x - 7)'( {x}^{2} - 3) - ( {x}^{2} - 3)'(x - 7)}{( {x}^{2} - 3) {}^{2} } = \\ = \frac{ {x}^{2} - 3 - 2x(x - 7)}{( {x}^{2} - 3) {}^{2} } = \frac{ {x}^{2} - 3 - 2 {x}^{2} + 14x}{( {x}^{2} - 3) {}^{2} } = \\ = \frac{ - {x}^{2} + 14x - 3}{( {x}^{2} - 3) {}^{2} } \\ x_{o} = 2 \\ f'(2) = \frac{ - 2 {}^{2} + 14 \times 2 - 3}{(2 {}^{2} - 3) {}^{2} } = \frac{ - 4 + 28 - 3}{(4 - 3) {}^{2} } = 21$