## 基本初等函數的導數公式 `$ C' = 0 $` `$ x^n = n x^{n-1} $` `$ (a^x)' =a^x \ln a $` `$ (e^x)' = e^x $` `$ (\log_a{x})' = \frac{1}{x\ln a} $` `$ (\log_{10}{x})' =(\lg{x})' = \frac{1}{x\ln 10} $` `$ (\ln{x})' = \frac{1}{x} $` `$ (sin x)' = cos x $` `$ (cos x)' = -sin x $` `$ (tan x)' = sec^2x $` `$ (cot x)' = -csc^2x $` `$ (sec x)' = secxtanx $` `$ (csc x)' = -cscx cotx $` #### 反三角函數 `$ (arcsinx)' = \frac {1} {\sqrt { 1- x^2} } $` `$ (arccosx)' = \frac {-1} {\sqrt { 1- x^2} } $` `$ (arctanx) '= \frac {1} {1+x^2} $` `$ (arccotx)' = \frac {-1} {1+x^2} $` ## 函數和差積上求導法則 `$ (u+v)'= u'+v' $` `$ (Cu)'=Cu' $` `$ (uv)'=u'v + uv' $` ```[math] (\frac u v)' = \frac {u'v-uv'}{v^2} ``` ```[math] ``` ```[math] ``` ```[math] ``` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $` `$ $`