39.5. Найдите производную функции:

Решение:

1. \( y = \frac{5}{3x - 2} \) \(\implies y' = \frac{0 \cdot (3x - 2) - 5 \cdot 3}{(3x - 2)^2} = \frac{-15}{(3x - 2)^2}\).
2. \( y = \frac{x^3}{\cos x} \) \(\implies y' = \frac{3x^2 \cos x - x^3 (-\sin x)}{\cos^2 x} = \frac{3x^2 \cos x + x^3 \sin x}{\cos^2 x}\).
3. \( y = \frac{3 - x^2}{4 + 2x} \) \(\implies y' = \frac{-2x(4 + 2x) - (3 - x^2)(2)}{(4 + 2x)^2} = \frac{-8x - 4x^2 - 6 + 2x^2}{(4 + 2x)^2} = \frac{-2x^2 - 8x - 6}{(4 + 2x)^2} = \frac{-2(x^2 + 4x + 3)}{(4 + 2x)^2}\).
4. \( y = \frac{x^2 - 5x}{x - 7} \) \(\implies y' = \frac{(2x - 5)(x - 7) - (x^2 - 5x)(1)}{(x - 7)^2} = \frac{2x^2 - 14x - 5x + 35 - x^2 + 5x}{(x - 7)^2} = \frac{x^2 - 14x + 35}{(x - 7)^2}\).

Ответ: 1) \( \frac{-15}{(3x - 2)^2} \) 2) \( \frac{3x^2 \cos x + x^3 \sin x}{\cos^2 x} \) 3) \( \frac{-2(x^2 + 4x + 3)}{(4 + 2x)^2} \) 4) \( \frac{x^2 - 14x + 35}{(x - 7)^2} \).