📝 题目
例 6 求 ${\left( \sin ax\right) }^{\prime },{\left( \tan bx\right) }^{\prime }$ 和 ${\left( {\mathrm{e}}^{cx}\right) }^{\prime }$ .
💡 答案与解析
解 为了求 ${\left( \sin ax\right) }^{\prime }$ ,我们在心目中把 $y = {ax}$ 当作中间变量,先对中间变量求导,再乘以这中间变量对 $x$ 的导数. 具体的书写格式如下:
$$ {\left( \sin ax\right) }^{\prime } = \left( {\cos {ax}}\right) \cdot {\left( ax\right) }^{\prime } = a\cos {ax}. $$
类似地可求得
$$ {\left( \tan bx\right) }^{\prime } = \frac{1}{{\cos }^{2}{bx}} \cdot {\left( bx\right) }^{\prime } = \frac{b}{{\cos }^{2}{bx}}. $$
$$ {\left( {\mathrm{e}}^{cx}\right) }^{\prime } = \left( {\mathrm{e}}^{cx}\right) \cdot {\left( cx\right) }^{\prime } = c{\mathrm{e}}^{cx}. $$