oscos2????xxxln)sin(sin2????xxx1cossin2???.cosx?.2sin1ln2cos2xxxx??下页上页首页《高等数学》电子教案杨庚华制作例3.tan的导数求xy?解)cossin()(tan?????xxxyxxxxx2cos)(cossincos)(sin????xxx222cossincos??os1??.sec)(tan2xx??即.csc)(cot2xx???同理可得下页上页首页《高等数学》电子教案杨庚华制作例4.sec的导数求xy?解)cos1()(sec?????xxyxx2cos)(cos???.tansecxx?xx2cossin?.cotcsc)(cscxxx???同理可得例5.sinh的导数求xy?解])(21[)(sinh???????xxeexy)(21xxee???.coshx?同理可得xxsinh)(cosh??xx2cosh1)(tanh??下页上页首页《高等数学》电子教案杨庚华制作例6).(,0),1ln(0,)(xfxxxxxf????????求设解,1)(??xf,0时当?x,0时当?xhxhxxfh)1ln()1ln(lim)(0???????)11ln(1lim0xhhh????,11x??下页上页首页《高等数学》电子教案杨庚华制作,0时当?xhhfh)01ln()0(lim)0(0????????,1?hhfh)01ln()]0(1ln[lim)0(0?????????,1?.1)0(???f.0,110,1)(???????????xxxxf下页上页首页《高等数学》电子教案杨庚华制作二、反函数的导数定理.)(1)(,)(,0)()(yxfIxfyyIyxxy??????????且有内也可导在对应区间那末它的反函数且内单调、可导在某区间如果函数即反函数的导数等于直接函数导数的倒数.下页上页首页