Теория:

[tex]\displaystyle (x^n)' = n*x^{n-1}[/tex]
Решение:

1) [tex]\displaystyle y=\frac{1}{x}[/tex]

[tex]\displaystyle y=x^{-1}[/tex]

[tex]\displaystyle y'=-1*x^{-1-1}[/tex]

[tex]\displaystyle y'=-1*x^{-2}[/tex]

[tex]\displaystyle y'=-\frac{1}{x^2}[/tex]

2) [tex]\displaystyle y = \sqrt{x}[/tex]

[tex]\displaystyle y = x^{1/2}[/tex]

[tex]\displaystyle y' =\frac{1}{2}*x^{0,5-1}[/tex]

[tex]\displaystyle y' =\frac{1}{2}*x^{-1/2}[/tex]

[tex]\displaystyle y' =\frac{1}{2\sqrt{x} }[/tex]