807. Найти f′(3) и f′(1), если: 1) f(x)=1/x+1/x²; 2) f(x)=√x+1/x+1; 3) f(x)=3/√x−2/x³; 4) f(x)=x^(3/2)−x^(−3/2).

1. Представим функцию в степенном виде: \(f(x)=x^{-1}+x^{-2}\).

   \(f'(x)=-x^{-2}-2x^{-3}\).

   \(f'(3)=-\frac{1}{9}-\frac{2}{27}=-\frac{5}{27}\), \(f'(1)=-1-2=-3\).

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

   \(f'(3)=\frac{1}{2\sqrt{3}}-\frac{1}{9}\), \(f'(1)=\frac12-1=-\frac12\).

3. \(f(x)=3x^{-1/2}-2x^{-3}\).

   \(f'(x)=-\frac32x^{-3/2}+6x^{-4}\).

   \(f'(3)=-\frac{1}{2\sqrt3}+\frac{2}{27}\), \(f'(1)=-\frac32+6=\frac92\).

4. \(f'(x)=\frac32x^{1/2}+\frac32x^{-5/2}\).

   \(f'(3)=\frac{3\sqrt3}{2}+\frac{1}{18\sqrt3}\), \(f'(1)=\frac32+\frac32=3\).

Ответ: 1) \(f'(3)=-\frac{5}{27}\), \(f'(1)=-3\); 2) \(f'(3)=\frac{1}{2\sqrt3}-\frac19\), \(f'(1)=-\frac12\); 3) \(f'(3)=-\frac{1}{2\sqrt3}+\frac{2}{27}\), \(f'(1)=\frac92\); 4) \(f'(3)=\frac{3\sqrt3}{2}+\frac{1}{18\sqrt3}\), \(f'(1)=3\).