📝 题目
例 8 求 ${\left( \sin {x}^{2}\right) }^{\prime }$ 和 ${\left( {\mathrm{e}}^{{x}^{2}}\right) }^{\prime }$ .
💡 答案与解析
解 我们有
$$ {\left( \sin {x}^{2}\right) }^{\prime } = \left( {\cos {x}^{2}}\right) \cdot {\left( {x}^{2}\right) }^{\prime } = {2x}\cos {x}^{2}, $$
$$ {\left( {\mathrm{e}}^{{x}^{2}}\right) }^{\prime } = \left( {\mathrm{e}}^{{x}^{2}}\right) \cdot {\left( {x}^{2}\right) }^{\prime } = {2x}{\mathrm{e}}^{{x}^{2}}. $$