导数公式

基本初等函数求导公式

  1. $(C)' = 0$
  2. $(x^u)'=ux^{u-1}$
  3. $(sin x)' = cos x $
  4. $(tan x)' = sec^2 x $
  5. $(cos x)' = -sin x $
  6. $(cot x)' = - csc^2 x$
  7. $(sec x)' =sec x * tan x$
  8. $(csc x)' = -csc x * cot x$
  9. $(a^x)' = a^x ln a$
  10. $(e^x)' = e^x$
  11. $(log_a x)' = {1 over xln a} $
  12. $(ln x)' = {1 over x}$
  13. $(arcsin x)' = {frac1{sqrt{1-x^2}} }$
  14. $(arccos x)' = {-frac1{sqrt{1-x^2}} }$
  15. $(arctan x)' = {frac1{1+x^2} }$
  16. $(arctan x)' = {-frac1{1+x^2} }$

函数求导法则

设 $z =z(x),f = f(x)$ 都可导,则:
1.$(u{pm}f)'=u'pm v'$
2.$(uv)'=u'v + uv'$
3.$(frac{u}{v})' = frac {u'v-uv'}{v^2}$

链式法则

设 $z =z(x),f = f(z)$ 都可导,则:
$frac{partial f}{partial x} = frac{partial f}{partial z} * frac{partial z}{partial x}$

矩阵转置求导(前导不变,后导转置)

$(AX)' = A^T$
$(XA)' = A$
$(x^TA)' = A$
$(Ax^T)' = A^T$