Hàm số \[y = {\tan ^2}\frac{x}{2}\] có đạo hàm là:

Bước 1:

\[\begin{array}{*{20}{l}}{{{\left( {{{\tan }^2}\frac{x}{2}} \right)}^\prime } = 2\tan \frac{x}{2}{{\left( {\tan \frac{x}{2}} \right)}^\prime }}\end{array}\]

Bước 2:

\[ = 2\tan \frac{x}{2}.\frac{{{{\left( {\frac{x}{2}} \right)}^\prime }}}{{{{\cos }^2}\frac{x}{2}}}\]

\[ = 2\tan \frac{x}{2}.\frac{{\frac{1}{2}}}{{{{\cos }^2}\frac{x}{2}}} = \frac{{\sin \frac{x}{2}}}{{\cos \frac{x}{2}}}.\frac{1}{{{{\cos }^2}\frac{x}{2}}} = \frac{{\sin \frac{x}{2}}}{{{{\cos }^3}\frac{x}{2}}}\]

Đáp án cần chọn là: C