Tính đạo hàm của các hàm số sau: c) y= tan x/2- cot x/2 ;

Trả lời

c) Ta có: $y^{\text{'}}={\left(\tan \frac{x}{2}-\cot \frac{x}{2}\right)}^{\text{'}}=\frac{{\left(\frac{x}{2}\right)}^{\text{'}}}{co{s}^2\frac{x}{2}}+\frac{{\left(\frac{x}{2}\right)}^{\text{'}}}{{\sin }^2\frac{x}{2}}$

$=\frac{\frac{1}{2}}{co{s}^2\frac{x}{2}}+\frac{\frac{1}{2}}{{\sin }^2\frac{x}{2}}==\frac{1}{2}\cdot \frac{{\sin }^2\frac{x}{2}+co{s}^2\frac{x}{2}}{{\sin }^2\frac{x}{2}co{s}^2\frac{x}{2}}$ $=\frac{2}{{\sin }^{2}x}$

Vậy $y^{\text{'}}=\frac{2}{{\sin }^{2}x}$  .