Tìm đạo hàm bằng định nghĩa tại x0 1.y=c (c là hằng số) 2.y=căn x 3.y=1/x 4. y-x^2

1) $y’=$ $\lim_{n \to x_{o}}  \dfrac{c-c}{x-x_{o}}$

=  $\lim_{n \to x_{o}}  \dfrac{0}{x-x_{o}}$

= $\lim_{n \to x_{o}}  0$ = $0$

.

2) $y’ =  \lim_{n \to x_{o}} \dfrac{\sqrt[]{x}-\sqrt[]{x_{o}}}{x-x_{o}}$  

=  $\lim_{n \to x_{o}} \dfrac{\sqrt[]{x}-\sqrt[]{x_{o}}}{(\sqrt[]{x}-\sqrt[]{x_{o}}).(\sqrt[]{x}+\sqrt[]{x_{o}})}$  
=  $\lim_{n \to x_{o}} \dfrac{1}{\sqrt[]{x}+\sqrt[]{x_{o}}}$

=  $ \dfrac{1}{\sqrt[]{x_{o}}+\sqrt[]{x_{o}}}$

=  $ \dfrac{1}{2\sqrt[]{x_{o}}}$

.

3) $y’=\lim_{n \to x_{o}}\dfrac{\dfrac{1}{x}-\dfrac{1}{x_{o}}}{x-x_{o}}$ 

$=\lim_{n \to x_{o}}\dfrac{\dfrac{x_{o}-x}{x.x_{o}}}{x-x_{o}}$ 

$=\lim_{n \to x_{o}}\dfrac{x_{o}-x}{x.x_{o}.(x-x_{o})}$ 

$=\lim_{n \to x_{o}}\dfrac{x_{o}-x}{x.x_{o}.(x-x_{o})}$  

$=\lim_{n \to x_{o}}\dfrac{1}{x.x_{o}}$  

$=\dfrac{1}{x_{o}.x_{o}}$  

$=\dfrac{1}{x_{o}^2}$ 

.

4) $y’=$$\lim_{n \to x_{o}}\dfrac{x^2-x_{o}^2}{x-x_{o}}$ 

$=\lim_{n \to x_{o}}\dfrac{(x-x_{o})(x+x_{o})}{x-x_{o}}$  

$=\lim_{n \to x_{o}}x+x_{o}$  

$=x_{o}+x_{o}$  

$=2x_{o}$