高端网站设计技术分析,Wordpress主页面增加,全网络品牌推广,做网站资源管理是Latex#xff1a;导数【高中常用公式】吴文中公式编辑器#xff1a;Ⅰ) 像码字一样Latex#xff0c;复杂公式轻松编辑#xff1b; Ⅱ)大学、高中、初中、小学常用公式#xff0c;一键模板。Note#xff1a;① 点击链接#xff0c;想怎么修改就怎么修改#xff1b;② 复…Latex导数【高中常用公式】吴文中公式编辑器Ⅰ) 像码字一样Latex复杂公式轻松编辑 Ⅱ)大学、高中、初中、小学常用公式一键模板。Note① 点击链接想怎么修改就怎么修改② 复制代码Latex代码一键获取导数的定义{f \prime { \left( {\mathop{{x}}\nolimits_{{0}}} \right) }\mathop{{ \text{lim} }}\limits_{{ \Delta x \to 0}}\frac{{ \Delta y}}{{ \Delta x}}\mathop{{ \text{lim} }}\limits_{{ \Delta x \to 0}}\frac{{f{ \left( {\mathop{{x}}\nolimits_{{0}} \Delta x} \right) }-f{ \left( {\mathop{{x}}\nolimits_{{0}}} \right) }}}{{ \Delta x}}}导数的记法\mathop{{\left. y \prime \right| }}\nolimits_{{x\mathop{{x}}\nolimits_{{0}}}}莱布尼兹记法\begin{array}{*{20}{l}}{\mathop{{\left. \frac{{ \text{d} y}}{{ \text{d} x}} \right| }}\nolimits_{{x\mathop{{x}}\nolimits_{{0}}}}}\\{\mathop{{\left. \frac{{ \text{d} f{ \left( {x} \right) }}}{{ \text{d} x}} \right| }}\nolimits_{{x\mathop{{x}}\nolimits_{{0}}}}}\end{array}牛顿记法\mathop{{\left. \dot {y} \right| }}\nolimits_{{x\mathop{{x}}\nolimits_{{0}}}}反函数求导法则\left[ {\mathop{{f}}\nolimits^{{-1}}{ \left( {x} \right) }} \left] \prime \frac{{1}}{{f \prime { \left( {y} \right) }}}\right. \right.复合函数求导法则\begin{array}{*{20}{l}}{yf{ \left( {u} \right) },ug{ \left( {x} \right) }}\\{\frac{{ \text{d} y}}{{ \text{d} x}}\frac{{ \text{d} y}}{{ \text{d} u}} \cdot \frac{{ \text{d} u}}{{ \text{d} x}}}\end{array}和差积商求导法则\begin{array}{*{20}{l}}{ \left( {u \pm v} \left) \prime {u \prime } \pm {v \prime }\right. \right. }\\{ \left( {Cu} \left) \prime C{u \prime }\right. \right. }\\{ \left( {uv} \left) \prime {u \prime }vu{v \prime }\right. \right. }\\{ \left( {\frac{{u}}{{v}}} \left) \prime \frac{{u \prime v-u{v \prime }}}{{\mathop{{v}}\nolimits^{{2}}}},{ \left( {v \neq 0} \right) }\right. \right. }\end{array}基本导数1\begin{array}{*{20}{l}}{ \left( {C} \left) \prime 0\right. \right. }\\{ \left( {\mathop{{x}}\nolimits^{{ \mu }}} \left) \prime \mu \mathop{{x}}\nolimits^{{ \mu -1}}\right. \right. }\end{array}基本导数2\begin{array}{*{20}{l}}{ \left( { \text{sin} x} \left) \prime \text{cos} x\right. \right. }\\{ \left( { \text{cos} x} \left) \prime - \text{sin} x\right. \right. }\\{ \left( { \text{tan} x} \left) \prime \mathop{{ \text{sec} }}\nolimits^{{2}}x\right. \right. }\\{ \left( { \text{cot} x} \left) \prime -\mathop{{ \text{csc} }}\nolimits^{{2}}x\right. \right. }\\{ \left( { \text{sec} x} \left) \prime \text{sec} x \text{tan} x\right. \right. }\\{ \left( { \text{csc} x} \left) \prime - \text{csc} x{ \text{cot} x}\right. \right. }\end{array}基本导数3\begin{array}{*{20}{l}}{ \left( {\mathop{{a}}\nolimits^{{x}}} \left) \prime \mathop{{a}}\nolimits^{{x}} \text{ln} a\right. \right. }\\{ \left( {\mathop{{e}}\nolimits^{{x}}} \left) \prime \mathop{{e}}\nolimits^{{x}}\right. \right. }\\{ \left( {\mathop{{ \text{log} }}\nolimits_{{a}}x} \left) \prime \frac{{1}}{{x \text{ln} a}}\right. \right. }\\{ \left( { \text{ln} a} \left) \prime \frac{{1}}{{x}}\right. \right. }\end{array}基本导数4\begin{array}{*{20}{l}}{ \left( { \text{arcsin} x} \left) \prime \frac{{1}}{{\sqrt{{1-\mathop{{x}}\nolimits^{{2}}}}}}\right. \right. }\\{ \left( { \text{arccos} x} \left) \prime -\frac{{1}}{{\sqrt{{1-\mathop{{x}}\nolimits^{{2}}}}}}\right. \right. }\\{ \left( { \text{arctan} x} \left) \prime \frac{{1}}{{1\mathop{{x}}\nolimits^{{2}}}}\right. \right. }\\{ \left( { \text{arccot} x} \left) \prime -\frac{{1}}{{1\mathop{{x}}\nolimits^{{2}}}}\right. \right. }\end{array}
