📝 题目
例 11 求 ${\left( {\mathrm{e}}^{\sin \left( {{x}^{2} + c}\right) }\right) }^{\prime }$ .
💡 答案与解析
解 我们有
$$ {\left( {\mathrm{e}}^{\sin \left( {{x}^{2} + c}\right) }\right) }^{\prime } = {\mathrm{e}}^{\sin \left( {{x}^{2} + c}\right) }{\left( \sin \left( {x}^{2} + c\right) \right) }^{\prime } $$
$$ = {\mathrm{e}}^{\sin \left( {{x}^{2} + c}\right) }\cos \left( {{x}^{2} + c}\right) {\left( {x}^{2} + c\right) }^{\prime } $$
$$ = {2x}\cos \left( {{x}^{2} + c}\right) {\mathrm{e}}^{\sin \left( {{x}^{2} + c}\right) }. $$