📝 题目
例 24 设 $y = {\mathrm{e}}^{\beta x}$ ,求 ${y}^{\left( n\right) }$ .
💡 答案与解析
解 ${y}^{\prime } = \beta {\mathrm{e}}^{\beta x},{y}^{\prime \prime } = {\beta }^{2}{\mathrm{e}}^{\beta x},\cdots ,{y}^{\left( n\right) } = {\beta }^{n}{\mathrm{e}}^{\beta x}$ .