Hàm số \(y = f\left( x \right) = \dfrac{2}{{\cot \left( {\pi x} \right)}}\) có \(f'\left( 3 \right)\) bằng:

* Hướng dẫn giải

\(\begin{array}{l}f'\left( x \right) = \dfrac{{ - 2\left( {\cot \left( {\pi x} \right)} \right)'}}{{{{\cot }^2}\left( {\pi x} \right)}} = \dfrac{{\dfrac{{2\pi }}{{{{\sin }^2}\left( {\pi x} \right)}}}}{{\dfrac{{{{\cos }^2}\left( {\pi x} \right)}}{{{{\sin }^2}\left( {\pi x} \right)}}}} = \dfrac{{2\pi }}{{{{\cos }^2}\left( {\pi x} \right)}}\\ \Rightarrow f'\left( 3 \right) = \dfrac{{2\pi }}{{{{\cos }^2}\left( {3\pi } \right)}} = 2\pi \end{array}\)

Chọn B