1) Найти производные функций a) f(x) = 5x³ – 4x⁹ б) f(x) = 6\(\sqrt[3]{x}\) + 4√x в) f(x) = \(\frac{x² + 2x - 3}{x}\) г) f(x) = 1/6 x³ + 0,5x² - 7x+1 д) f(x) = 2x√x е) f(x) = \(\frac{4 - 3x}{x + 2}\) ж) f(x) = cos(5 – 3x)

1) Найти производные функций:

1. a) \( f(x) = 5x^3 - 4x^9 \)
   \( f'(x) = 15x^2 - 36x^8 \)
2. б) \( f(x) = 6\sqrt[3]{x} + 4\sqrt{x} = 6x^{1/3} + 4x^{1/2} \)
   \( f'(x) = 6 \cdot \frac{1}{3}x^{-2/3} + 4 \cdot \frac{1}{2}x^{-1/2} = 2x^{-2/3} + 2x^{-1/2} = \frac{2}{\sqrt[3]{x^2}} + \frac{2}{\sqrt{x}} \)
3. в) \( f(x) = \frac{x^2 + 2x - 3}{x} = x + 2 - \frac{3}{x} \)
   \( f'(x) = 1 - 3(-1)x^{-2} = 1 + \frac{3}{x^2} \)
4. г) \( f(x) = \frac{1}{6}x^3 + 0.5x^2 - 7x + 1 \)
   \( f'(x) = \frac{1}{6} \cdot 3x^2 + 0.5 \cdot 2x - 7 = \frac{1}{2}x^2 + x - 7 \)
5. д) \( f(x) = 2x\sqrt{x} = 2x^{3/2} \)
   \( f'(x) = 2 \cdot \frac{3}{2}x^{1/2} = 3\sqrt{x} \)
6. е) \( f(x) = \frac{4 - 3x}{x + 2} \)
   \( f'(x) = \frac{-3(x+2) - (4-3x)(1)}{(x+2)^2} = \frac{-3x - 6 - 4 + 3x}{(x+2)^2} = \frac{-10}{(x+2)^2} \)
7. ж) \( f(x) = \cos(5 - 3x) \)
   \( f'(x) = -\sin(5 - 3x) \cdot (-3) = 3\sin(5 - 3x) \)