39.2. Найдите производную функции:

Решение:

1. \( y = 2x^5 - x \) \(\implies y' = 10x^4 - 1\)
2. \( y = x^7 - 4\sqrt{x} \) \(\implies y' = 7x^6 - \frac{4}{2\sqrt{x}} = 7x^6 - \frac{2}{\sqrt{x}}\).
3. \( y = \sin x + 2\cos x \) \(\implies y' = \cos x - 2\sin x\)
4. \( y = x - \frac{5}{x} \) \(\implies y' = 1 - 5(-\frac{1}{x^2}) = 1 + \frac{5}{x^2}\)
5. \( y = 12 - \mathrm{ctg} x \) \(\implies y' = -(-\frac{1}{\sin^2 x}) = \frac{1}{\sin^2 x}\)
6. \( y = 0,4x^{-5} + \sqrt{3} \) \(\implies y' = 0,4(-5)x^{-6} = -2x^{-6} = -\frac{2}{x^6}\)

Ответ: 1) \( 10x^4 - 1 \) 2) \( 7x^6 - \frac{2}{\sqrt{x}} \) 3) \( \cos x - 2\sin x \) 4) \( 1 + \frac{5}{x^2} \) 5) \( \frac{1}{\sin^2 x} \) 6) \( -\frac{2}{x^6} \).