z.B.
a)
$$f'(x_0)= \lim_{x\to x_0} \frac{f(x) - f(x_0)}{x - x_0} \\=\lim_{x\to x_0} \frac{\frac{1}{x^2}-\frac{1}{x_0^2}}{x - x_0} \\=\lim_{x\to x_0} \frac{\frac{x_0^2-x^2}{x^2x_0^2}}{x-x_0} \\=\lim_{x\to x_0} - \frac{\frac{x^2-x_0^2}{x^2x_0^2}}{x-x_0} \\=\lim_{x\to x_0}-\frac{x+x_0}{x^2x_0^2} \\= - \frac{2x_0}{x_0^4} \\= -\frac{2}{x_0^3}$$
b)
$$ f'(x_0) = \lim_{x\to x_0} \frac{f(x) - f(x_0)}{x - x_0} \\=\lim_{x\to x_0} \frac{\sqrt{x} - \sqrt{x_0}}{x - x_0}\\=\lim_{x\to x_0} \frac{\sqrt{x} - \sqrt{x_0}}{(\sqrt{x} - \sqrt{x_0})(\sqrt{x} + \sqrt{x_0})}$$
Schaffst du den Rest alleine?