📝 题目
例 12 求 ${\left( \ln \left| \sin {x}^{2}\right| \right) }^{\prime }$ .
💡 答案与解析
解 我们有
$$ {\left( \ln \left| \sin {x}^{2}\right| \right) }^{\prime } = \frac{1}{\sin {x}^{2}}{\left( \sin {x}^{2}\right) }^{\prime } $$
$$ = \frac{1}{\sin {x}^{2}}\cos {x}^{2}{\left( {x}^{2}\right) }^{\prime } $$
$$ = {2x}\cot {x}^{2}\;\left( {x \neq \sqrt{k\pi }}\right) . $$