1) Найти производные функций a) f(x) = -2x^7 + 3x^3 б) f(x) = 12√(x - 4√x) в) f(x) = (1-2x+3x^2)/x г) f(x) = -1/9 x^3 +1,5x^2 +5x + 12 д) f(x) = -x√x е) f(x) = (3+2x)/(x-5) ж) f(x) = sin(3 - 2x)

1) Производные функций:

1. a) \( f'(x) = -14x^6 + 9x^2 \)


2. б) \( f'(x) = 12 \cdot \frac{1}{2\sqrt{x}} - 4 \cdot \frac{1}{2\sqrt{x}} = \frac{6}{\sqrt{x}} - \frac{2}{\sqrt{x}} = \frac{4}{\sqrt{x}} \)


3. в) \( f(x) = \frac{1}{x} - 2 + 3x \). \( f'(x) = -\frac{1}{x^2} + 3 \)


4. г) \( f'(x) = -\frac{1}{3} x^2 + 3x + 5 \)


5. д) \( f(x) = -x^{3/2} \). \( f'(x) = -\frac{3}{2} x^{1/2} = -\frac{3}{2} \sqrt{x} \)


6. е) \( f'(x) = \frac{2(x-5) - (3+2x)}{(x-5)^2} = \frac{2x-10-3-2x}{(x-5)^2} = \frac{-13}{(x-5)^2} \)


7. ж) \( f'(x) = \cos(3-2x) \cdot (-2) = -2\cos(3-2x) \)