微积分公式温习
表
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(三角函数,指数函数,反三角函数)(微分公式)(积分公式)[新版]
公 式 複 習
Differentiation Rules(微分公式) Integration Rules(積分公式)
n,1 dxnn,1nn, , ,xnx ,,,, , if 1xdxCn,dx,1n
d11 dxxC,,lnln , 0xx,,,xdxx
d11lnx where logx,,logx,aalnadxxaln
dsincosxdxxC,,,,sincosxx, dxcossinxdxxC,,,d cossinxx,,2sectanxdxxC,,dx, 2dcsccotxdxxC,,,2,tansecxx, 三 dxsectansecxxdxxC,,,角 d2cotcscxx,, csccotcscxxdxxC,,,函 dx,
數 dtanlncoslnsecxdxxCxC,,,,,secsectanxxx, ,dx
cotlnsinlncscxdxxCxC,,,,,,d csccsccotxxx,, dxseclnsectanxdxxxC,,,,
csclncsccotxdxxxC,,,,
dxxxx指 edxeC,, ee, ,dx數 xdaxxx函 ln , 0aaaa,, , 0, 1adxCaa,,,, ,dxlna數
d11x,1,1x,1, , ,,, sinxdxCasin , 0反 ,222dxa,,1xax三 d111x,1,1x, ,,,,tanxdxCatan , 0 , 角 222,,,dxx1axaa函 d111x,1,1x,1 , ,secx,,, dxCasec , 0數 ,222dxaa,||1xx,xxa
d,,kfxdxkfxdx()(), fxgxfxgxfxgx()()()()()(),, ,,dx
,,,,dfxfxgxfxgx()()()()(),[()()]()()fxgxdxfxdxgxdx,,, ,,,2,,,dxgxgx()(()),,
(The Chain Rule) (鏈鎖律) (The Substitution Rule) (代換法)
ugx,()d,,[(())](())()fgxfgxgx,, , fgxgxdxfudu(())()(),,,dx
ugx,()bgb(),fgxgxdxfudu(())()(), ,,aga()