文档介绍：第九讲导数的四则运算重点:导数的四则运算法则和基本初等函数的求导公式难点:两个函数乘积和商的求导法则的应用一、、差、积、商的求导法则设uux?(),vvx?(),则(1)vuvu??????)((2)uccu???)((c是常数)(3)vuvuuv?????)((4)2vvuvuvu???????????u?????)()((C是常数)。推论2wuvwvuvwuuvw???????)(。推论321vvv??????????。推论1表明,求一个常数乘以一个函数的导数,可以把常数提到导数符号外面来。推论2表明,求三个函数乘积的导数,等于每次只对其中的一个函数求导数并与另外两个函数相乘的和。例11sincos53)(4????xexxfx,求)(xf?及)0(f?。解)(xf?=)1sincos53(4????xexx=)1(sin)cos5()()3(4???????xexx=)1(sin)(cos5)()(34???????xexx=0)sin(5123????xexx=xexxsin5123??)0(f?=1|)(0????xxf。例2)cos(sinxxeyx??,求y?。解y?=)cos(sin)cos(sin)(?????xxexxexx=)sin(cos)cos(sinxxexxexx???=xexcos2例3设112???xxy,求y?。解y?=?????????112xx=2222)1()1)(1()1()1(????????xxxxx=222)1(2)1()1(1??????xxxx=222)1(12????xxx。例4设xytan?,求y?。解y?=)(tan?x=???????xxcossin=xxxxx2cos)(cossincos)(sin???=xxx222cossincos?=x2cos1=x2sec。即)(tan?x=x2sec。同理)(cot?x=x2csc?。例5设xysec?,求y?。解y?=)(sec?x=???????xcos1=xxx2cos)(cos1cos)1(????=xx2cossin=xxtansec,