Tìm đạo hàm của hàm số \(g\left( \varphi \right) = \frac{{\cos \varphi + \sin \varphi }}{{1 - \cos \varphi }}\)
\(\begin{array}{l}
g(\varphi ) = \frac{{\cos \varphi + \sin \varphi }}{{1 - \cos \varphi }}\\
\Rightarrow g\prime (\varphi ) = \frac{{(\cos \varphi + \sin \varphi )\prime (1 - \cos \varphi ) - (\cos \varphi + \sin \varphi )(1 - \cos \varphi )\prime }}{{{{(1 - \cos \varphi )}^2}}}\\
= \frac{{( - \sin \varphi + \cos \varphi )(1 - \cos \varphi ) - (\cos \varphi + \sin \varphi )(\sin \varphi )}}{{{{(1 - \cos \varphi )}^2}}}\\
= \frac{{ - \sin \varphi + \cos \varphi + \sin \varphi \cos \varphi - \cos 2\varphi - \sin \varphi \cos \varphi - {{\sin }^2}\varphi }}{{{{(1 - \cos \varphi )}^2}}}\\
= \frac{{\cos \varphi - \sin \varphi - 1}}{{{{(1 - \cos \varphi )}^2}}}
\end{array}\)
-- Mod Toán 11