📝 题目
例 14 求 ${\left( \ln \left( x + \sqrt{{x}^{2} \pm {a}^{2}}\right) \right) }^{\prime }$ .
💡 答案与解析
解 我们有
$$ {\left( \ln \left( x + \sqrt{{x}^{2} \pm {a}^{2}}\right) \right) }^{\prime } = \frac{1}{x + \sqrt{{x}^{2} \pm {a}^{2}}}{\left( x + \sqrt{{x}^{2} \pm {a}^{2}}\right) }^{\prime } $$
$$ = \frac{1}{x + \sqrt{{x}^{2} \pm {a}^{2}}}\left( {1 + \frac{x}{\sqrt{{x}^{2} \pm {a}^{2}}}}\right) $$
$$ = \frac{1}{\sqrt{{x}^{2} \pm {a}^{2}}}. $$